LMFDB - Embedded newform 462.2.u.a.349.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(13,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("462.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.u (of order $10$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.2
Character	$\chi$	$=$	462.349
Dual form			462.2.u.a.139.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.884493 + 1.21740i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-1.60058 - 2.10669i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.884493 + 1.21740i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-1.60058 - 2.10669i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +1.50479 q^{10} +(2.41443 - 2.27388i) q^{11} -1.00000i q^{12} +(-2.55126 + 1.85360i) q^{13} +(-0.763555 + 2.53318i) q^{14} +(0.465006 - 1.43114i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.63949 + 2.64424i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(1.96491 + 6.04736i) q^{19} +(-0.884493 - 1.21740i) q^{20} +(2.17324 + 1.50898i) q^{21} +(-3.25877 - 0.616760i) q^{22} +8.51382 q^{23} +(-0.809017 + 0.587785i) q^{24} +(0.845349 + 2.60172i) q^{25} +(2.99918 + 0.974493i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.49819 - 0.871235i) q^{28} +(0.814675 + 0.264704i) q^{29} +(-1.43114 + 0.465006i) q^{30} +(3.69441 + 5.08492i) q^{31} +1.00000i q^{32} +(-1.59359 + 2.90869i) q^{33} -4.49865i q^{34} +(3.98039 - 0.0851877i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-1.85973 + 5.72367i) q^{37} +(3.73748 - 5.14420i) q^{38} +(1.85360 - 2.55126i) q^{39} +(-0.465006 + 1.43114i) q^{40} +(-3.11905 - 9.59944i) q^{41} +(-0.0566111 - 2.64515i) q^{42} -8.65762i q^{43} +(1.41649 + 2.99893i) q^{44} +1.50479i q^{45} +(-5.00430 - 6.88783i) q^{46} +(1.41837 - 0.460858i) q^{47} +(0.951057 + 0.309017i) q^{48} +(-1.87631 + 6.74385i) q^{49} +(1.60795 - 2.21315i) q^{50} +(-4.27847 - 1.39016i) q^{51} +(-0.974493 - 2.99918i) q^{52} +(0.331296 - 0.240700i) q^{53} +1.00000 q^{54} +(0.632679 + 4.95056i) q^{55} +(-2.17324 - 1.50898i) q^{56} +(-3.73748 - 5.14420i) q^{57} +(-0.264704 - 0.814675i) q^{58} +(5.04243 + 1.63838i) q^{59} +(1.21740 + 0.884493i) q^{60} +(5.80756 + 4.21944i) q^{61} +(1.94227 - 5.97769i) q^{62} +(-2.53318 - 0.763555i) q^{63} +(0.809017 - 0.587785i) q^{64} -4.74539i q^{65} +(3.28987 - 0.420443i) q^{66} -10.5366 q^{67} +(-3.63949 + 2.64424i) q^{68} +(-8.09712 + 2.63092i) q^{69} +(-2.40853 - 3.17013i) q^{70} +(11.6159 + 8.43945i) q^{71} +(0.587785 - 0.809017i) q^{72} +(4.34451 - 13.3710i) q^{73} +(5.72367 - 1.85973i) q^{74} +(-1.60795 - 2.21315i) q^{75} -6.35857 q^{76} +(-8.65485 - 1.44694i) q^{77} -3.15352 q^{78} +(7.69909 + 10.5969i) q^{79} +(1.43114 - 0.465006i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.93278 + 8.16577i) q^{82} +(-2.08119 - 1.51207i) q^{83} +(-2.10669 + 1.60058i) q^{84} +(-6.43820 + 2.09190i) q^{85} +(-7.00417 + 5.08882i) q^{86} -0.856600 q^{87} +(1.59359 - 2.90869i) q^{88} +2.90093i q^{89} +(1.21740 - 0.884493i) q^{90} +(7.98844 + 2.40789i) q^{91} +(-2.63092 + 8.09712i) q^{92} +(-5.08492 - 3.69441i) q^{93} +(-1.20654 - 0.876604i) q^{94} +(-9.10001 - 2.95677i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-9.52282 - 13.1070i) q^{97} +(6.55875 - 2.44597i) q^{98} +(0.616760 - 3.25877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	$ 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) $ 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$2$	−0.587785	−	0.809017i	−0.415627	−	0.572061i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$3$	−0.951057	+	0.309017i	−0.549093	+	0.178411i
$4$	−0.309017	+	0.951057i	−0.154508	+	0.475528i
$5$	−0.884493	+	1.21740i	−0.395557	+	0.544438i	−0.959622	−	0.281293i	$-0.909237\pi$
$5$	−0.884493	+	1.21740i	−0.395557	+	0.544438i	0.564065	+	0.825731i	$0.309237\pi$
$6$	0.809017	+	0.587785i	0.330280	+	0.239962i
$7$	−1.60058	−	2.10669i	−0.604961	−	0.796255i
$7$	−1.60058	−	2.10669i	−0.604961	−	0.796255i
$8$	0.951057	−	0.309017i	0.336249	−	0.109254i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	1.50479			0.475856
$11$	2.41443	−	2.27388i	0.727978	−	0.685601i
$11$	2.41443	−	2.27388i	0.727978	−	0.685601i
$12$		−	1.00000i		−	0.288675i
$13$	−2.55126	+	1.85360i	−0.707591	+	0.514095i	−0.882396	−	0.470508i	$-0.844071\pi$
$13$	−2.55126	+	1.85360i	−0.707591	+	0.514095i	0.174805	+	0.984603i	$0.444071\pi$
$14$	−0.763555	+	2.53318i	−0.204069	+	0.677020i
$15$	0.465006	−	1.43114i	0.120064	−	0.369519i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	3.63949	+	2.64424i	0.882705	+	0.641323i	0.933966	−	0.357362i	$-0.116324\pi$
$17$	3.63949	+	2.64424i	0.882705	+	0.641323i	−0.0512605	+	0.998685i	$0.516324\pi$
$18$	−0.951057	−	0.309017i	−0.224166	−	0.0728360i
$19$	1.96491	+	6.04736i	0.450781	+	1.38736i	0.876018	+	0.482279i	$0.160191\pi$
$19$	1.96491	+	6.04736i	0.450781	+	1.38736i	−0.425237	+	0.905082i	$0.639809\pi$
$20$	−0.884493	−	1.21740i	−0.197779	−	0.272219i
$21$	2.17324	+	1.50898i	0.474240	+	0.329286i
$22$	−3.25877	−	0.616760i	−0.694773	−	0.131494i
$23$	8.51382			1.77525			0.887627	−	0.460563i	$-0.152352\pi$
$23$	8.51382			1.77525			0.887627	+	0.460563i	$0.152352\pi$
$24$	−0.809017	+	0.587785i	−0.165140	+	0.119981i
$25$	0.845349	+	2.60172i	0.169070	+	0.520344i
$26$	2.99918	+	0.974493i	0.588188	+	0.191114i
$27$	−0.587785	+	0.809017i	−0.113119	+	0.155695i
$28$	2.49819	−	0.871235i	0.472113	−	0.164648i
$29$	0.814675	+	0.264704i	0.151281	+	0.0491543i	0.383679	−	0.923467i	$-0.374657\pi$
$29$	0.814675	+	0.264704i	0.151281	+	0.0491543i	−0.232397	+	0.972621i	$0.574657\pi$
$30$	−1.43114	+	0.465006i	−0.261289	+	0.0848980i
$31$	3.69441	+	5.08492i	0.663536	+	0.913279i	0.999592	−	0.0285628i	$-0.00909305\pi$
$31$	3.69441	+	5.08492i	0.663536	+	0.913279i	−0.336056	+	0.941842i	$0.609093\pi$
$32$			1.00000i			0.176777i
$33$	−1.59359	+	2.90869i	−0.277408	+	0.506338i
$34$		−	4.49865i		−	0.771513i
$35$	3.98039	−	0.0851877i	0.672808	−	0.0143994i
$36$	0.309017	+	0.951057i	0.0515028	+	0.158509i
$37$	−1.85973	+	5.72367i	−0.305738	+	0.940965i	0.673663	+	0.739039i	$0.264720\pi$
$37$	−1.85973	+	5.72367i	−0.305738	+	0.940965i	−0.979401	+	0.201926i	$0.935280\pi$
$38$	3.73748	−	5.14420i	0.606299	−	0.834499i
$39$	1.85360	−	2.55126i	0.296813	−	0.408528i
$40$	−0.465006	+	1.43114i	−0.0735238	+	0.226283i
$41$	−3.11905	−	9.59944i	−0.487113	−	1.49918i	−0.828897	−	0.559402i	$-0.811031\pi$
$41$	−3.11905	−	9.59944i	−0.487113	−	1.49918i	0.341784	−	0.939779i	$-0.388969\pi$
$42$	−0.0566111	−	2.64515i	−0.00873528	−	0.408155i
$43$		−	8.65762i		−	1.32028i	−0.751145	−	0.660138i	$-0.770498\pi$
$43$		−	8.65762i		−	1.32028i	0.751145	−	0.660138i	$-0.229502\pi$
$44$	1.41649	+	2.99893i	0.213544	+	0.452105i
$45$			1.50479i			0.224321i
$46$	−5.00430	−	6.88783i	−0.737843	−	1.01555i
$47$	1.41837	−	0.460858i	0.206891	−	0.0672230i	−0.203738	−	0.979025i	$-0.565309\pi$
$47$	1.41837	−	0.460858i	0.206891	−	0.0672230i	0.410629	+	0.911802i	$0.365309\pi$
$48$	0.951057	+	0.309017i	0.137273	+	0.0446028i
$49$	−1.87631	+	6.74385i	−0.268044	+	0.963407i
$50$	1.60795	−	2.21315i	0.227398	−	0.312987i
$51$	−4.27847	−	1.39016i	−0.599106	−	0.194661i
$52$	−0.974493	−	2.99918i	−0.135138	−	0.415912i
$53$	0.331296	−	0.240700i	0.0455070	−	0.0330627i	−0.564799	−	0.825228i	$-0.691046\pi$
$53$	0.331296	−	0.240700i	0.0455070	−	0.0330627i	0.610306	+	0.792166i	$0.291046\pi$
$54$	1.00000			0.136083
$55$	0.632679	+	4.95056i	0.0853104	+	0.667533i
$56$	−2.17324	−	1.50898i	−0.290412	−	0.201646i
$57$	−3.73748	−	5.14420i	−0.495041	−	0.681365i
$58$	−0.264704	−	0.814675i	−0.0347573	−	0.106972i
$59$	5.04243	+	1.63838i	0.656468	+	0.213299i	0.618264	−	0.785971i	$-0.287836\pi$
$59$	5.04243	+	1.63838i	0.656468	+	0.213299i	0.0382041	+	0.999270i	$0.487836\pi$
$60$	1.21740	+	0.884493i	0.157166	+	0.114188i
$61$	5.80756	+	4.21944i	0.743582	+	0.540244i	0.893831	−	0.448404i	$-0.148007\pi$
$61$	5.80756	+	4.21944i	0.743582	+	0.540244i	−0.150249	+	0.988648i	$0.548007\pi$
$62$	1.94227	−	5.97769i	0.246668	−	0.759167i
$63$	−2.53318	−	0.763555i	−0.319150	−	0.0961988i
$64$	0.809017	−	0.587785i	0.101127	−	0.0734732i
$65$		−	4.74539i		−	0.588593i
$66$	3.28987	−	0.420443i	0.404955	−	0.0517530i
$67$	−10.5366			−1.28725			−0.643624	−	0.765341i	$-0.722570\pi$
$67$	−10.5366			−1.28725			−0.643624	+	0.765341i	$0.722570\pi$
$68$	−3.63949	+	2.64424i	−0.441353	+	0.320661i
$69$	−8.09712	+	2.63092i	−0.974779	+	0.316725i
$70$	−2.40853	−	3.17013i	−0.287875	−	0.378903i
$71$	11.6159	+	8.43945i	1.37855	+	1.00158i	0.997014	+	0.0772259i	$0.0246063\pi$
$71$	11.6159	+	8.43945i	1.37855	+	1.00158i	0.381540	+	0.924352i	$0.375394\pi$
$72$	0.587785	−	0.809017i	0.0692712	−	0.0953436i
$73$	4.34451	−	13.3710i	0.508486	−	1.56496i	−0.286344	−	0.958127i	$-0.592440\pi$
$73$	4.34451	−	13.3710i	0.508486	−	1.56496i	0.794830	−	0.606832i	$-0.207560\pi$
$74$	5.72367	−	1.85973i	0.665363	−	0.216189i
$75$	−1.60795	−	2.21315i	−0.185670	−	0.255553i
$76$	−6.35857			−0.729379
$77$	−8.65485	−	1.44694i	−0.986311	−	0.164894i
$78$	−3.15352			−0.357066
$79$	7.69909	+	10.5969i	0.866215	+	1.19224i	0.980052	+	0.198743i	$0.0636859\pi$
$79$	7.69909	+	10.5969i	0.866215	+	1.19224i	−0.113837	+	0.993499i	$0.536314\pi$
$80$	1.43114	−	0.465006i	0.160006	−	0.0519892i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−5.93278	+	8.16577i	−0.655166	+	0.901758i
$83$	−2.08119	−	1.51207i	−0.228440	−	0.165972i	0.467677	−	0.883899i	$-0.345091\pi$
$83$	−2.08119	−	1.51207i	−0.228440	−	0.165972i	−0.696118	+	0.717928i	$0.745091\pi$
$84$	−2.10669	+	1.60058i	−0.229859	+	0.174637i
$85$	−6.43820	+	2.09190i	−0.698321	+	0.226898i
$86$	−7.00417	+	5.08882i	−0.755279	+	0.548742i
$87$	−0.856600			−0.0918372
$88$	1.59359	−	2.90869i	0.169877	−	0.310067i
$89$			2.90093i			0.307498i	0.988110	+	0.153749i	$0.0491348\pi$
$89$			2.90093i			0.307498i	−0.988110	+	0.153749i	$0.950865\pi$
$90$	1.21740	−	0.884493i	0.128325	−	0.0932338i
$91$	7.98844	+	2.40789i	0.837416	+	0.252415i
$92$	−2.63092	+	8.09712i	−0.274292	+	0.844184i
$93$	−5.08492	−	3.69441i	−0.527282	−	0.383093i
$94$	−1.20654	−	0.876604i	−0.124445	−	0.0904148i
$95$	−9.10001	−	2.95677i	−0.933642	−	0.303359i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	−9.52282	−	13.1070i	−0.966896	−	1.33082i	−0.943599	−	0.331090i	$-0.892584\pi$
$97$	−9.52282	−	13.1070i	−0.966896	−	1.33082i	−0.0232969	−	0.999729i	$-0.507416\pi$
$98$	6.55875	−	2.44597i	0.662534	−	0.247080i
$99$	0.616760	−	3.25877i	0.0619867	−	0.327519i
$100$	−2.73561			−0.273561
$101$	−14.9282	+	10.8460i	−1.48542	+	1.07922i	−0.509655	+	0.860379i	$0.670227\pi$
$101$	−14.9282	+	10.8460i	−1.48542	+	1.07922i	−0.975761	+	0.218839i	$0.929773\pi$
$102$	1.39016	+	4.27847i	0.137646	+	0.423632i
$103$	−5.25796	−	1.70842i	−0.518082	−	0.168335i	0.0382925	−	0.999267i	$-0.487808\pi$
$103$	−5.25796	−	1.70842i	−0.518082	−	0.168335i	−0.556375	+	0.830931i	$0.687808\pi$
$104$	−1.85360	+	2.55126i	−0.181760	+	0.250171i
$105$	−3.75925	+	1.31103i	−0.366865	+	0.127943i
$106$	−0.389461	−	0.126544i	−0.0378278	−	0.0122910i
$107$	−1.60651	+	0.521987i	−0.155307	+	0.0504623i	−0.385639	−	0.922650i	$-0.626019\pi$
$107$	−1.60651	+	0.521987i	−0.155307	+	0.0504623i	0.230332	+	0.973112i	$0.426019\pi$
$108$	−0.587785	−	0.809017i	−0.0565597	−	0.0778477i
$109$			2.23434i			0.214011i	0.994258	+	0.107006i	$0.0341263\pi$
$109$			2.23434i			0.214011i	−0.994258	+	0.107006i	$0.965874\pi$
$110$	3.63321	−	3.42171i	0.346413	−	0.326248i
$111$		−	6.01822i		−	0.571224i
$112$	0.0566111	+	2.64515i	0.00534924	+	0.249943i
$113$	3.27813	+	10.0890i	0.308380	+	0.949098i	0.978394	+	0.206749i	$0.0662882\pi$
$113$	3.27813	+	10.0890i	0.308380	+	0.949098i	−0.670014	+	0.742349i	$0.733712\pi$
$114$	−1.96491	+	6.04736i	−0.184030	+	0.566388i
$115$	−7.53042	+	10.3647i	−0.702215	+	0.966516i
$116$	−0.503497	+	0.693004i	−0.0467485	+	0.0643438i
$117$	−0.974493	+	2.99918i	−0.0900919	+	0.277274i
$118$	−1.63838	−	5.04243i	−0.150825	−	0.464193i
$119$	−0.254674	−	11.8996i	−0.0233459	−	1.09083i
$120$		−	1.50479i		−	0.137368i
$121$	0.658928	−	10.9802i	0.0599025	−	0.998204i
$122$		−	7.17854i		−	0.649915i
$123$	5.93278	+	8.16577i	0.534941	+	0.736283i
$124$	−5.97769	+	1.94227i	−0.536812	+	0.174421i
$125$	−11.0707	−	3.59710i	−0.990197	−	0.321734i
$126$	0.871235	+	2.49819i	0.0776158	+	0.222556i
$127$	−3.41815	+	4.70468i	−0.303312	+	0.417473i	−0.933281	−	0.359147i	$-0.883068\pi$
$127$	−3.41815	+	4.70468i	−0.303312	+	0.417473i	0.629969	+	0.776620i	$0.283068\pi$
$128$	−0.951057	−	0.309017i	−0.0840623	−	0.0273135i
$129$	2.67535	+	8.23389i	0.235552	+	0.724954i
$130$	−3.83910	+	2.78927i	−0.336712	+	0.244635i
$131$	15.5441			1.35810			0.679048	−	0.734094i	$-0.262393\pi$
$131$	15.5441			1.35810			0.679048	+	0.734094i	$0.262393\pi$
$132$	−2.27388	−	2.41443i	−0.197916	−	0.210149i
$133$	9.59495	−	13.8187i	0.831988	−	1.19824i
$134$	6.19325	+	8.52428i	0.535015	+	0.736385i
$135$	−0.465006	−	1.43114i	−0.0400213	−	0.123173i
$136$	4.27847	+	1.39016i	0.366876	+	0.119205i
$137$	11.3520	+	8.24771i	0.969867	+	0.704650i	0.955421	−	0.295246i	$-0.0954016\pi$
$137$	11.3520	+	8.24771i	0.969867	+	0.704650i	0.0144457	+	0.999896i	$0.495402\pi$
$138$	6.88783	+	5.00430i	0.586331	+	0.425994i
$139$	4.71121	−	14.4996i	0.399600	−	1.22984i	−0.525721	−	0.850657i	$-0.676204\pi$
$139$	4.71121	−	14.4996i	0.399600	−	1.22984i	0.925321	−	0.379185i	$-0.123796\pi$
$140$	−1.14899	+	3.81190i	−0.0971073	+	0.322164i
$141$	−1.20654	+	0.876604i	−0.101609	+	0.0738234i
$142$		−	14.3580i		−	1.20490i
$143$	−1.94497	+	10.2766i	−0.162646	+	0.859375i
$144$	−1.00000			−0.0833333
$145$	−1.04283	+	0.757657i	−0.0866019	+	0.0629200i
$146$	−13.3710	+	4.34451i	−1.10659	+	0.359554i
$147$	−0.299489	−	6.99359i	−0.0247014	−	0.576822i
$148$	−4.86884	−	3.53742i	−0.400216	−	0.290774i
$149$	−2.55934	+	3.52263i	−0.209669	+	0.288585i	−0.900880	−	0.434068i	$-0.857078\pi$
$149$	−2.55934	+	3.52263i	−0.209669	+	0.288585i	0.691211	+	0.722653i	$0.257078\pi$
$150$	−0.845349	+	2.60172i	−0.0690225	+	0.212429i
$151$	3.60628	−	1.17175i	0.293475	−	0.0953557i	−0.158579	−	0.987346i	$-0.550691\pi$
$151$	3.60628	−	1.17175i	0.293475	−	0.0953557i	0.452054	+	0.891990i	$0.350691\pi$
$152$	3.73748	+	5.14420i	0.303149	+	0.417249i
$153$	4.49865			0.363695
$154$	3.91660	+	7.85241i	0.315608	+	0.632765i
$155$	−9.45807			−0.759691
$156$	1.85360	+	2.55126i	0.148406	+	0.204264i
$157$	0.954725	−	0.310209i	0.0761953	−	0.0247574i	−0.270671	−	0.962672i	$-0.587246\pi$
$157$	0.954725	−	0.310209i	0.0761953	−	0.0247574i	0.346867	+	0.937914i	$0.387246\pi$
$158$	4.04765	−	12.4574i	0.322014	−	0.991056i
$159$	−0.240700	+	0.331296i	−0.0190888	+	0.0262735i
$160$	−1.21740	−	0.884493i	−0.0962440	−	0.0699253i
$161$	−13.6270	−	17.9360i	−1.07396	−	1.41355i
$162$	−0.951057	+	0.309017i	−0.0747221	+	0.0242787i
$163$	−6.11694	+	4.44422i	−0.479116	+	0.348098i	−0.800983	−	0.598687i	$-0.795690\pi$
$163$	−6.11694	+	4.44422i	−0.479116	+	0.348098i	0.321867	+	0.946785i	$0.395690\pi$
$164$	10.0934			0.788166
$165$	−2.13152	−	4.51275i	−0.165939	−	0.351317i
$166$			2.57249i			0.199664i
$167$	−0.695150	+	0.505056i	−0.0537924	+	0.0390824i	−0.614357	−	0.789029i	$-0.710584\pi$
$167$	−0.695150	+	0.505056i	−0.0537924	+	0.0390824i	0.560564	+	0.828111i	$0.310584\pi$
$168$	2.53318	+	0.763555i	0.195439	+	0.0589095i
$169$	−0.944133	+	2.90574i	−0.0726257	+	0.223519i
$170$	5.47666	+	3.97903i	0.420041	+	0.305178i
$171$	5.14420	+	3.73748i	0.393386	+	0.285812i
$172$	8.23389	+	2.67535i	0.627828	+	0.203994i
$173$	−0.992527	−	3.05468i	−0.0754604	−	0.232243i	0.906211	−	0.422827i	$-0.138962\pi$
$173$	−0.992527	−	3.05468i	−0.0754604	−	0.232243i	−0.981671	+	0.190583i	$0.938962\pi$
$174$	0.503497	+	0.693004i	0.0381700	+	0.0525365i
$175$	4.12797	−	5.94514i	0.312045	−	0.449410i
$176$	−3.28987	+	0.420443i	−0.247983	+	0.0316921i
$177$	−5.30192			−0.398517
$178$	2.34690	−	1.70513i	0.175908	−	0.127805i
$179$	−5.09035	−	15.6665i	−0.380470	−	1.17097i	−0.939713	−	0.341963i	$-0.888908\pi$
$179$	−5.09035	−	15.6665i	−0.380470	−	1.17097i	0.559243	−	0.829004i	$-0.311092\pi$
$180$	−1.43114	−	0.465006i	−0.106671	−	0.0346595i
$181$	−1.82414	+	2.51071i	−0.135587	+	0.186620i	−0.871412	−	0.490553i	$-0.836795\pi$
$181$	−1.82414	+	2.51071i	−0.135587	+	0.186620i	0.735824	+	0.677172i	$0.236795\pi$
$182$	−2.74746	−	7.87810i	−0.203655	−	0.583964i
$183$	−6.82720	−	2.21829i	−0.504681	−	0.163981i
$184$	8.09712	−	2.63092i	0.596928	−	0.193954i
$185$	−5.32307	−	7.32658i	−0.391360	−	0.538661i
$186$			6.28531i			0.460861i
$187$	14.8000	−	1.89143i	1.08228	−	0.138315i
$188$			1.49137i			0.108769i
$189$	2.64515	−	0.0566111i	0.192406	−	0.00411785i
$190$	2.95677	+	9.10001i	0.214507	+	0.660184i
$191$	3.82986	−	11.7871i	0.277119	−	0.852885i	−0.711532	−	0.702654i	$-0.751998\pi$
$191$	3.82986	−	11.7871i	0.277119	−	0.852885i	0.988651	−	0.150231i	$-0.0480018\pi$
$192$	−0.587785	+	0.809017i	−0.0424197	+	0.0583858i
$193$	−9.43680	+	12.9886i	−0.679276	+	0.934943i	−0.999925	−	0.0122552i	$-0.996099\pi$
$193$	−9.43680	+	12.9886i	−0.679276	+	0.934943i	0.320649	+	0.947198i	$0.396099\pi$
$194$	−5.00644	+	15.4083i	−0.359442	+	1.10625i
$195$	1.46641	+	4.51314i	0.105012	+	0.323192i
$196$	−5.83397	−	3.86844i	−0.416712	−	0.276317i
$197$		−	1.60878i		−	0.114621i	−0.998356	−	0.0573103i	$-0.981748\pi$
$197$		−	1.60878i		−	0.114621i	0.998356	−	0.0573103i	$-0.0182524\pi$
$198$	−2.99893	+	1.41649i	−0.213124	+	0.100666i
$199$			11.0985i			0.786749i	0.919378	+	0.393374i	$0.128692\pi$
$199$			11.0985i			0.786749i	−0.919378	+	0.393374i	$0.871308\pi$
$200$	1.60795	+	2.21315i	0.113699	+	0.156494i
$201$	10.0209	−	3.25598i	0.706819	−	0.229659i
$202$	17.5492	+	5.70208i	1.23476	+	0.401197i
$203$	−0.746300	−	2.13995i	−0.0523800	−	0.150195i
$204$	2.64424	−	3.63949i	0.185134	−	0.254815i
$205$	14.4451	+	4.69351i	1.00889	+	0.327809i
$206$	1.70842	+	5.25796i	0.119031	+	0.366339i
$207$	6.88783	−	5.00430i	0.478737	−	0.347823i
$208$	3.15352			0.218658
$209$	18.4951	+	10.1330i	1.27933	+	0.700911i
$210$	3.27027	+	2.27070i	0.225670	+	0.156693i
$211$	−3.84349	−	5.29012i	−0.264597	−	0.364187i	0.655959	−	0.754796i	$-0.272264\pi$
$211$	−3.84349	−	5.29012i	−0.264597	−	0.364187i	−0.920556	+	0.390610i	$0.872264\pi$
$212$	0.126544	+	0.389461i	0.00869106	+	0.0267483i
$213$	−13.6553	−	4.43688i	−0.935647	−	0.304010i
$214$	1.36658	+	0.992877i	0.0934174	+	0.0678717i
$215$	10.5398	+	7.65761i	0.718808	+	0.522245i
$216$	−0.309017	+	0.951057i	−0.0210259	+	0.0647112i
$217$	4.79918	−	15.9218i	0.325789	−	1.08084i
$218$	1.80762	−	1.31331i	0.122428	−	0.0889488i
$219$			14.0591i			0.950027i
$220$	−4.90377	−	0.928094i	−0.330612	−	0.0625721i
$221$	−14.1866			−0.954295
$222$	−4.86884	+	3.53742i	−0.326775	+	0.237416i
$223$	−3.76532	+	1.22343i	−0.252144	+	0.0819266i	−0.432362	−	0.901700i	$-0.642320\pi$
$223$	−3.76532	+	1.22343i	−0.252144	+	0.0819266i	0.180218	+	0.983627i	$0.442320\pi$
$224$	2.10669	−	1.60058i	0.140759	−	0.106943i
$225$	2.21315	+	1.60795i	0.147544	+	0.107197i
$226$	6.23537	−	8.58225i	0.414771	−	0.570883i
$227$	2.73353	−	8.41294i	0.181431	−	0.558386i	−0.818438	−	0.574595i	$-0.805160\pi$
$227$	2.73353	−	8.41294i	0.181431	−	0.558386i	0.999869	+	0.0162086i	$0.00515958\pi$
$228$	6.04736	−	1.96491i	0.400496	−	0.130129i
$229$	14.0839	+	19.3849i	0.930693	+	1.28099i	0.959588	+	0.281407i	$0.0908011\pi$
$229$	14.0839	+	19.3849i	0.930693	+	1.28099i	−0.0288951	+	0.999582i	$0.509199\pi$
$230$	12.8115			0.844766
$231$	8.67838	−	1.29838i	0.570995	−	0.0854269i
$232$	0.856600			0.0562385
$233$	−7.93086	−	10.9159i	−0.519568	−	0.715124i	0.465928	−	0.884823i	$-0.345721\pi$
$233$	−7.93086	−	10.9159i	−0.519568	−	0.715124i	−0.985496	+	0.169699i	$0.945721\pi$
$234$	2.99918	−	0.974493i	0.196063	−	0.0637046i
$235$	−0.693494	+	2.13436i	−0.0452386	+	0.139230i
$236$	−3.11639	+	4.28934i	−0.202860	+	0.279213i
$237$	−10.5969	−	7.69909i	−0.688342	−	0.500109i
$238$	−9.47728	+	7.20044i	−0.614321	+	0.466735i
$239$	20.1326	−	6.54148i	1.30227	−	0.423133i	0.425899	−	0.904771i	$-0.359958\pi$
$239$	20.1326	−	6.54148i	1.30227	−	0.423133i	0.876371	+	0.481637i	$0.159958\pi$
$240$	−1.21740	+	0.884493i	−0.0785829	+	0.0570938i
$241$	6.58131			0.423940			0.211970	−	0.977276i	$-0.432012\pi$
$241$	6.58131			0.423940			0.211970	+	0.977276i	$0.432012\pi$
$242$	−9.27051	+	5.92094i	−0.595931	+	0.380613i
$243$			1.00000i			0.0641500i
$244$	−5.80756	+	4.21944i	−0.371791	+	0.270122i
$245$	−6.55038	−	8.24910i	−0.418489	−	0.527016i
$246$	3.11905	−	9.59944i	0.198863	−	0.612038i
$247$	−16.2223	−	11.7862i	−1.03220	−	0.749940i
$248$	5.08492	+	3.69441i	0.322893	+	0.234595i
$249$	2.44659	+	0.794944i	0.155046	+	0.0503775i
$250$	3.59710	+	11.0707i	0.227501	+	0.700175i
$251$	3.79479	+	5.22307i	0.239525	+	0.329678i	0.911808	−	0.410616i	$-0.134686\pi$
$251$	3.79479	+	5.22307i	0.239525	+	0.329678i	−0.672284	+	0.740294i	$0.734686\pi$
$252$	1.50898	−	2.17324i	0.0950567	−	0.136901i
$253$	20.5560	−	19.3594i	1.29235	−	1.21712i
$254$	5.81530			0.364885
$255$	5.47666	−	3.97903i	0.342962	−	0.249176i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−4.20208	−	1.36534i	−0.262118	−	0.0851674i	0.175010	−	0.984567i	$-0.444004\pi$
$257$	−4.20208	−	1.36534i	−0.262118	−	0.0851674i	−0.437128	+	0.899399i	$0.644004\pi$
$258$	5.08882	−	7.00417i	0.316816	−	0.436060i
$259$	15.0346	−	5.24328i	0.934208	−	0.325802i
$260$	4.51314	+	1.46641i	0.279893	+	0.0909427i
$261$	0.814675	−	0.264704i	0.0504271	−	0.0163848i
$262$	−9.13660	−	12.5755i	−0.564461	−	0.776914i
$263$		−	17.5189i		−	1.08026i	−0.841581	−	0.540130i	$-0.818375\pi$
$263$		−	17.5189i		−	1.08026i	0.841581	−	0.540130i	$-0.181625\pi$
$264$	−0.616760	+	3.25877i	−0.0379589	+	0.200564i
$265$			0.616217i			0.0378539i
$266$	−16.8194	+	0.359966i	−1.03126	+	0.0220709i
$267$	−0.896437	−	2.75895i	−0.0548611	−	0.168845i
$268$	3.25598	−	10.0209i	0.198891	−	0.612123i
$269$	−12.5706	+	17.3020i	−0.766444	+	1.05492i	0.230207	+	0.973142i	$0.426060\pi$
$269$	−12.5706	+	17.3020i	−0.766444	+	1.05492i	−0.996651	+	0.0817776i	$0.973940\pi$
$270$	−0.884493	+	1.21740i	−0.0538285	+	0.0740886i
$271$	7.34658	−	22.6105i	0.446273	−	1.37349i	−0.434808	−	0.900523i	$-0.643184\pi$
$271$	7.34658	−	22.6105i	0.446273	−	1.37349i	0.881082	−	0.472964i	$-0.156816\pi$
$272$	−1.39016	−	4.27847i	−0.0842909	−	0.259421i
$273$	−8.34153	+	0.178524i	−0.504853	+	0.0108048i
$274$		−	14.0318i		−	0.847695i
$275$	7.95703	+	4.35944i	0.479827	+	0.262884i
$276$		−	8.51382i		−	0.512472i
$277$	16.2303	+	22.3391i	0.975183	+	1.34222i	0.939384	+	0.342866i	$0.111398\pi$
$277$	16.2303	+	22.3391i	0.975183	+	1.34222i	0.0357989	+	0.999359i	$0.488602\pi$
$278$	−14.4996	+	4.71121i	−0.869630	+	0.282560i
$279$	5.97769	+	1.94227i	0.357875	+	0.116281i
$280$	3.75925	−	1.31103i	0.224658	−	0.0783488i
$281$	3.00103	−	4.13057i	0.179027	−	0.246409i	−0.710067	−	0.704134i	$-0.751335\pi$
$281$	3.00103	−	4.13057i	0.179027	−	0.246409i	0.889094	+	0.457725i	$0.151335\pi$
$282$	1.41837	+	0.460858i	0.0844630	+	0.0274437i
$283$	8.40921	+	25.8809i	0.499876	+	1.53846i	0.809218	+	0.587508i	$0.199891\pi$
$283$	8.40921	+	25.8809i	0.499876	+	1.53846i	−0.309342	+	0.950951i	$0.600109\pi$
$284$	−11.6159	+	8.43945i	−0.689277	+	0.500789i
$285$	9.56832			0.566778
$286$	9.45719	−	4.46694i	0.559215	−	0.264136i
$287$	−15.2308	+	21.9355i	−0.899045	+	1.29481i
$288$	0.587785	+	0.809017i	0.0346356	+	0.0476718i
$289$	1.00056	+	3.07941i	0.0588565	+	0.181142i
$290$	1.22591	+	0.398324i	0.0719882	+	0.0233904i
$291$	13.1070	+	9.52282i	0.768348	+	0.558238i
$292$	11.3741	+	8.26374i	0.665617	+	0.483599i
$293$	2.65801	−	8.18053i	0.155283	−	0.477911i	−0.842907	−	0.538060i	$-0.819157\pi$
$293$	2.65801	−	8.18053i	0.155283	−	0.477911i	0.998189	+	0.0601484i	$0.0191574\pi$
$294$	−5.48190	+	4.35302i	−0.319711	+	0.253873i
$295$	−6.45456	+	4.68951i	−0.375799	+	0.273034i
$296$			6.01822i			0.349802i
$297$	0.420443	+	3.28987i	0.0243966	+	0.190897i
$298$	4.35421			0.252233
$299$	−21.7209	+	15.7812i	−1.25615	+	0.912649i
$300$	2.60172	−	0.845349i	0.150210	−	0.0488063i
$301$	−18.2390	+	13.8572i	−1.05128	+	0.798715i
$302$	−3.06768	−	2.22880i	−0.176525	−	0.128253i
$303$	10.8460	−	14.9282i	0.623087	−	0.857605i
$304$	1.96491	−	6.04736i	0.112695	−	0.346840i
$305$	−10.2735	+	3.33806i	−0.588259	+	0.191137i
$306$	−2.64424	−	3.63949i	−0.151161	−	0.208056i
$307$	−12.9569			−0.739491			−0.369745	−	0.929133i	$-0.620555\pi$
$307$	−12.9569			−0.739491			−0.369745	+	0.929133i	$0.620555\pi$
$308$	4.05061	−	7.78412i	0.230805	−	0.443541i
$309$	5.52855			0.314508
$310$	5.55932	+	7.65174i	0.315748	+	0.434590i
$311$	3.97992	−	1.29315i	0.225681	−	0.0733280i	−0.193994	−	0.981003i	$-0.562144\pi$
$311$	3.97992	−	1.29315i	0.225681	−	0.0733280i	0.419675	+	0.907675i	$0.362144\pi$
$312$	0.974493	−	2.99918i	0.0551698	−	0.169795i
$313$	3.80426	−	5.23612i	0.215030	−	0.295963i	−0.687853	−	0.725850i	$-0.741447\pi$
$313$	3.80426	−	5.23612i	0.215030	−	0.295963i	0.902883	+	0.429887i	$0.141447\pi$
$314$	−0.812137	−	0.590052i	−0.0458316	−	0.0332986i
$315$	3.17013	−	2.40853i	0.178617	−	0.135705i
$316$	−12.4574	+	4.04765i	−0.700783	+	0.227698i
$317$	−21.0946	+	15.3261i	−1.18479	+	0.860800i	−0.992704	−	0.120578i	$-0.961525\pi$
$317$	−21.0946	+	15.3261i	−1.18479	+	0.860800i	−0.192086	+	0.981378i	$0.561525\pi$
$318$	0.409504			0.0229638
$319$	2.56888	−	1.21337i	0.143830	−	0.0679354i
$320$			1.50479i			0.0841203i
$321$	1.36658	−	0.992877i	0.0762750	−	0.0554170i
$322$	−6.50077	+	21.5670i	−0.362274	+	1.20188i
$323$	−8.83944	+	27.2050i	−0.491840	+	1.51373i
$324$	0.809017	+	0.587785i	0.0449454	+	0.0326547i
$325$	−6.97923	−	5.07071i	−0.387138	−	0.281272i
$326$	7.19090	+	2.33647i	0.398267	+	0.129405i
$327$	−0.690450	−	2.12499i	−0.0381820	−	0.117512i
$328$	−5.93278	−	8.16577i	−0.327583	−	0.450879i
$329$	−3.24110	−	2.25044i	−0.178688	−	0.124071i
$330$	−2.39802	+	4.37697i	−0.132007	+	0.240944i
$331$	11.8981			0.653976			0.326988	−	0.945028i	$-0.393966\pi$
$331$	11.8981			0.653976			0.326988	+	0.945028i	$0.393966\pi$
$332$	2.08119	−	1.51207i	0.114220	−	0.0829858i
$333$	1.85973	+	5.72367i	0.101913	+	0.313655i
$334$	0.817198	+	0.265524i	0.0447151	+	0.0145288i
$335$	9.31954	−	12.8272i	0.509181	−	0.700827i
$336$	−0.871235	−	2.49819i	−0.0475298	−	0.136287i
$337$	−9.81697	−	3.18973i	−0.534764	−	0.173755i	0.0291709	−	0.999574i	$-0.490713\pi$
$337$	−9.81697	−	3.18973i	−0.534764	−	0.173755i	−0.563935	+	0.825819i	$0.690713\pi$
$338$	2.90574	−	0.944133i	0.158052	−	0.0513541i
$339$	−6.23537	−	8.58225i	−0.338659	−	0.466124i
$340$		−	6.76953i		−	0.367129i
$341$	20.4824	+	3.87653i	1.10918	+	0.209926i
$342$		−	6.35857i		−	0.343832i
$343$	17.2104	−	6.84124i	0.929274	−	0.369392i
$344$	−2.67535	−	8.23389i	−0.144245	−	0.443942i
$345$	3.95897	−	12.1845i	0.213144	−	0.655990i
$346$	−1.88790	+	2.59847i	−0.101494	+	0.139695i
$347$	7.84518	−	10.7980i	0.421151	−	0.579665i	−0.544743	−	0.838603i	$-0.683373\pi$
$347$	7.84518	−	10.7980i	0.421151	−	0.579665i	0.965894	+	0.258938i	$0.0833727\pi$
$348$	0.264704	−	0.814675i	0.0141896	−	0.0436712i
$349$	−2.60259	−	8.00994i	−0.139313	−	0.428762i	0.856923	−	0.515445i	$-0.172373\pi$
$349$	−2.60259	−	8.00994i	−0.139313	−	0.428762i	−0.996236	+	0.0866829i	$0.972373\pi$
$350$	−7.23608	+	0.154866i	−0.386785	+	0.00827792i
$351$		−	3.15352i		−	0.168323i
$352$	2.27388	+	2.41443i	0.121198	+	0.128689i
$353$		−	15.3281i		−	0.815831i	−0.913020	−	0.407915i	$-0.866256\pi$
$353$		−	15.3281i		−	0.815831i	0.913020	−	0.407915i	$-0.133744\pi$
$354$	3.11639	+	4.28934i	0.165634	+	0.227976i
$355$	−20.5484	+	6.67657i	−1.09059	+	0.354356i
$356$	−2.75895	−	0.896437i	−0.146224	−	0.0475111i
$357$	3.91939	+	11.2385i	0.207436	+	0.594804i
$358$	−9.68241	+	13.3267i	−0.511731	+	0.704338i
$359$	−24.3852	−	7.92322i	−1.28700	−	0.418172i	−0.415960	−	0.909383i	$-0.636554\pi$
$359$	−24.3852	−	7.92322i	−1.28700	−	0.418172i	−0.871040	+	0.491211i	$0.836554\pi$
$360$	0.465006	+	1.43114i	0.0245079	+	0.0754277i
$361$	−17.3384	+	12.5971i	−0.912549	+	0.663006i
$362$	3.10341			0.163112
$363$	2.76641	+	10.6465i	0.145199	+	0.558794i
$364$	−4.75860	+	6.85338i	−0.249418	+	0.359214i
$365$	12.4352	+	17.1156i	0.650888	+	0.895870i
$366$	2.21829	+	6.82720i	0.115952	+	0.356864i
$367$	−5.10461	−	1.65859i	−0.266459	−	0.0865777i	0.172741	−	0.984967i	$-0.444738\pi$
$367$	−5.10461	−	1.65859i	−0.266459	−	0.0865777i	−0.439199	+	0.898390i	$0.644738\pi$
$368$	−6.88783	−	5.00430i	−0.359053	−	0.260867i
$369$	−8.16577	−	5.93278i	−0.425093	−	0.308848i
$370$	−2.79851	+	8.61291i	−0.145487	+	0.447764i
$371$	−1.03735	−	0.312679i	−0.0538563	−	0.0162335i
$372$	5.08492	−	3.69441i	0.263641	−	0.191546i
$373$			26.7233i			1.38368i	0.722051	+	0.691840i	$0.243200\pi$
$373$			26.7233i			1.38368i	−0.722051	+	0.691840i	$0.756800\pi$
$374$	−10.2294	−	10.8617i	−0.528950	−	0.561644i
$375$	11.6405			0.601111
$376$	1.20654	−	0.876604i	0.0622226	−	0.0452074i
$377$	−2.56910	+	0.834750i	−0.132315	+	0.0429918i
$378$	−1.60058	−	2.10669i	−0.0823248	−	0.108357i
$379$	−13.3770	−	9.71895i	−0.687130	−	0.499229i	0.188586	−	0.982057i	$-0.439610\pi$
$379$	−13.3770	−	9.71895i	−0.687130	−	0.499229i	−0.875715	+	0.482828i	$0.839610\pi$
$380$	5.62412	−	7.74093i	0.288511	−	0.397101i
$381$	1.79703	−	5.53068i	0.0920645	−	0.283345i
$382$	−11.7871	+	3.82986i	−0.603081	+	0.195953i
$383$	−16.8091	−	23.1357i	−0.858905	−	1.18218i	−0.981830	−	0.189765i	$-0.939227\pi$
$383$	−16.8091	−	23.1357i	−0.858905	−	1.18218i	0.122925	−	0.992416i	$-0.460773\pi$
$384$	1.00000			0.0510310
$385$	9.41665	−	9.25661i	0.479917	−	0.471761i
$386$	16.0548			0.817170
$387$	−5.08882	−	7.00417i	−0.258679	−	0.356042i
$388$	15.4083	−	5.00644i	0.782235	−	0.254164i
$389$	2.23758	−	6.88657i	0.113450	−	0.349163i	−0.878171	−	0.478347i	$-0.841236\pi$
$389$	2.23758	−	6.88657i	0.113450	−	0.349163i	0.991621	+	0.129185i	$0.0412360\pi$
$390$	2.78927	−	3.83910i	0.141240	−	0.194401i
$391$	30.9859	+	22.5126i	1.56703	+	1.13851i
$392$	0.299489	+	6.99359i	0.0151265	+	0.353230i
$393$	−14.7833	+	4.80340i	−0.745720	+	0.242299i
$394$	−1.30153	+	0.945615i	−0.0655700	+	0.0476394i
$395$	−19.7104			−0.991740
$396$	2.90869	+	1.59359i	0.146167	+	0.0800809i
$397$		−	7.72319i		−	0.387616i	−0.981039	−	0.193808i	$-0.937916\pi$
$397$		−	7.72319i		−	0.387616i	0.981039	−	0.193808i	$-0.0620839\pi$
$398$	8.97884	−	6.52351i	0.450069	−	0.326994i
$399$	−4.85512	+	16.1074i	−0.243060	+	0.806378i
$400$	0.845349	−	2.60172i	0.0422675	−	0.130086i
$401$	12.6437	+	9.18622i	0.631398	+	0.458738i	0.856884	−	0.515509i	$-0.172397\pi$
$401$	12.6437	+	9.18622i	0.631398	+	0.458738i	−0.225486	+	0.974246i	$0.572397\pi$
$402$	−8.52428	−	6.19325i	−0.425152	−	0.308891i
$403$	−18.8508	−	6.12499i	−0.939024	−	0.305108i
$404$	−5.70208	−	17.5492i	−0.283689	−	0.873105i
$405$	0.884493	+	1.21740i	0.0439508	+	0.0604931i
$406$	−1.29259	+	1.86160i	−0.0641502	+	0.0923896i
$407$	8.52475	+	18.0482i	0.422556	+	0.894616i
$408$	−4.49865			−0.222717
$409$	−17.8144	+	12.9429i	−0.880865	+	0.639986i	−0.933480	−	0.358629i	$-0.883244\pi$
$409$	−17.8144	+	12.9429i	−0.880865	+	0.639986i	0.0526152	+	0.998615i	$0.483244\pi$
$410$	−4.69351	−	14.4451i	−0.231796	−	0.713394i
$411$	−13.3451	−	4.33608i	−0.658264	−	0.213883i
$412$	3.24960	−	4.47269i	0.160096	−	0.220354i
$413$	−4.61922	−	13.2452i	−0.227297	−	0.651754i
$414$	−8.09712	−	2.63092i	−0.397952	−	0.129302i
$415$	3.68160	−	1.19622i	0.180723	−	0.0587203i
$416$	−1.85360	−	2.55126i	−0.0908800	−	0.125086i
$417$			15.2458i			0.746590i
$418$	−2.67342	−	20.9189i	−0.130761	−	1.02318i
$419$			30.3705i			1.48369i	0.670569	+	0.741847i	$0.266050\pi$
$419$			30.3705i			1.48369i	−0.670569	+	0.741847i	$0.733950\pi$
$420$	−0.0851877	−	3.98039i	−0.00415674	−	0.194223i
$421$	−7.82723	−	24.0897i	−0.381476	−	1.17406i	−0.939005	−	0.343905i	$-0.888250\pi$
$421$	−7.82723	−	24.0897i	−0.381476	−	1.17406i	0.557528	−	0.830158i	$-0.311750\pi$
$422$	−2.02064	+	6.21891i	−0.0983635	+	0.302732i
$423$	0.876604	−	1.20654i	0.0426219	−	0.0586641i
$424$	0.240700	−	0.331296i	0.0116894	−	0.0160891i
$425$	−3.80293	+	11.7042i	−0.184469	+	0.567738i
$426$	4.43688	+	13.6553i	0.214968	+	0.661602i
$427$	−0.406385	−	18.9883i	−0.0196663	−	0.918908i
$428$		−	1.68918i		−	0.0816498i
$429$	−1.32588	−	10.3747i	−0.0640140	−	0.500894i
$430$		−	13.0279i		−	0.628261i
$431$	−1.90642	−	2.62396i	−0.0918290	−	0.126392i	0.760630	−	0.649185i	$-0.224890\pi$
$431$	−1.90642	−	2.62396i	−0.0918290	−	0.126392i	−0.852459	+	0.522793i	$0.824890\pi$
$432$	0.951057	−	0.309017i	0.0457577	−	0.0148676i
$433$	28.9345	+	9.40139i	1.39050	+	0.451802i	0.906108	−	0.423047i	$-0.139039\pi$
$433$	28.9345	+	9.40139i	1.39050	+	0.451802i	0.484396	+	0.874849i	$0.339039\pi$
$434$	−15.7019	+	5.47599i	−0.753715	+	0.262856i
$435$	0.757657	−	1.04283i	0.0363269	−	0.0499996i
$436$	−2.12499	−	0.690450i	−0.101768	−	0.0330665i
$437$	16.7289	+	51.4862i	0.800250	+	2.46292i
$438$	11.3741	−	8.26374i	0.543474	−	0.394857i
$439$	−12.1525			−0.580007			−0.290003	−	0.957026i	$-0.593656\pi$
$439$	−12.1525			−0.580007			−0.290003	+	0.957026i	$0.593656\pi$
$440$	2.13152	+	4.51275i	0.101616	+	0.215137i
$441$	2.44597	+	6.55875i	0.116475	+	0.312322i
$442$	8.33868	+	11.4772i	0.396631	+	0.545915i
$443$	−2.34990	−	7.23226i	−0.111647	−	0.343615i	0.879586	−	0.475740i	$-0.157820\pi$
$443$	−2.34990	−	7.23226i	−0.111647	−	0.343615i	−0.991233	+	0.132125i	$0.957820\pi$
$444$	5.72367	+	1.85973i	0.271633	+	0.0882590i
$445$	−3.53160	−	2.56586i	−0.167414	−	0.121633i
$446$	3.20297	+	2.32709i	0.151665	+	0.110191i
$447$	1.34552	−	4.14110i	0.0636411	−	0.195867i
$448$	−2.53318	−	0.763555i	−0.119681	−	0.0360746i
$449$	5.89723	−	4.28459i	0.278307	−	0.202202i	−0.439871	−	0.898061i	$-0.644976\pi$
$449$	5.89723	−	4.28459i	0.278307	−	0.202202i	0.718179	+	0.695859i	$0.244976\pi$
$450$		−	2.73561i		−	0.128958i
$451$	−29.3587	−	16.0848i	−1.38245	−	0.757404i
$452$	−10.6082			−0.498970
$453$	−3.06768	+	2.22880i	−0.144132	+	0.104718i
$454$	−8.41294	+	2.73353i	−0.394839	+	0.128291i
$455$	−9.99708	+	7.59537i	−0.468670	+	0.356076i
$456$	−5.14420	−	3.73748i	−0.240899	−	0.175023i
$457$	6.96844	−	9.59124i	0.325970	−	0.448659i	−0.614308	−	0.789066i	$-0.710565\pi$
$457$	6.96844	−	9.59124i	0.325970	−	0.448659i	0.940278	+	0.340407i	$0.110565\pi$
$458$	7.40437	−	22.7883i	0.345983	−	1.06483i
$459$	−4.27847	+	1.39016i	−0.199702	+	0.0648871i
$460$	−7.53042	−	10.3647i	−0.351107	−	0.483258i
$461$	−29.7426			−1.38525			−0.692624	−	0.721298i	$-0.743546\pi$
$461$	−29.7426			−1.38525			−0.692624	+	0.721298i	$0.743546\pi$
$462$	−6.15143	−	6.25779i	−0.286190	−	0.291139i
$463$	−22.1232			−1.02815			−0.514077	−	0.857744i	$-0.671865\pi$
$463$	−22.1232			−1.02815			−0.514077	+	0.857744i	$0.671865\pi$
$464$	−0.503497	−	0.693004i	−0.0233743	−	0.0321719i
$465$	8.99516	−	2.92271i	0.417141	−	0.135537i
$466$	−4.16950	+	12.8324i	−0.193148	+	0.594449i
$467$	23.4373	−	32.2586i	1.08455	−	1.49275i	0.230132	−	0.973160i	$-0.426084\pi$
$467$	23.4373	−	32.2586i	1.08455	−	1.49275i	0.854415	−	0.519591i	$-0.173916\pi$
$468$	−2.55126	−	1.85360i	−0.117932	−	0.0856825i
$469$	16.8646	+	22.1973i	0.778736	+	1.02498i
$470$	2.13436	−	0.693494i	0.0984505	−	0.0319885i
$471$	−0.812137	+	0.590052i	−0.0374213	+	0.0271882i
$472$	5.30192			0.244041
$473$	−19.6864	−	20.9032i	−0.905182	−	0.961131i
$474$			13.0985i			0.601633i
$475$	−14.0725	+	10.2243i	−0.645691	+	0.469122i
$476$	11.3959	+	3.43497i	0.522330	+	0.157441i
$477$	0.126544	−	0.389461i	0.00579404	−	0.0178322i
$478$	−17.1258	−	12.4426i	−0.783317	−	0.569113i
$479$	−31.7729	−	23.0844i	−1.45174	−	1.05475i	−0.985420	−	0.170137i	$-0.945579\pi$
$479$	−31.7729	−	23.0844i	−1.45174	−	1.05475i	−0.466322	−	0.884615i	$-0.654421\pi$
$480$	1.43114	+	0.465006i	0.0653223	+	0.0212245i
$481$	−5.86471	−	18.0497i	−0.267408	−	0.822997i
$482$	−3.86840	−	5.32440i	−0.176201	−	0.242520i
$483$	18.5026	+	12.8472i	0.841897	+	0.584566i
$484$	10.2392	+	4.01976i	0.465419	+	0.182716i
$485$	24.3794			1.10701
$486$	0.809017	−	0.587785i	0.0366978	−	0.0266625i
$487$	−0.896567	−	2.75935i	−0.0406273	−	0.125038i	0.928686	−	0.370868i	$-0.120940\pi$
$487$	−0.896567	−	2.75935i	−0.0406273	−	0.125038i	−0.969313	+	0.245830i	$0.920940\pi$
$488$	6.82720	+	2.21829i	0.309053	+	0.100417i
$489$	4.44422	−	6.11694i	0.200975	−	0.276618i
$490$	−2.82345	+	10.1481i	−0.127550	+	0.458443i
$491$	6.55664	+	2.13038i	0.295897	+	0.0961428i	0.453204	−	0.891407i	$-0.350281\pi$
$491$	6.55664	+	2.13038i	0.295897	+	0.0961428i	−0.157306	+	0.987550i	$0.550281\pi$
$492$	−9.59944	+	3.11905i	−0.432776	+	0.140617i
$493$	2.26506	+	3.11758i	0.102013	+	0.140409i
$494$			20.0519i			0.902179i
$495$	3.42171	+	3.63321i	0.153795	+	0.163301i
$496$		−	6.28531i		−	0.282219i
$497$	−0.812824	−	37.9791i	−0.0364601	−	1.70360i
$498$	−0.794944	−	2.44659i	−0.0356223	−	0.109634i
$499$	−13.4740	+	41.4687i	−0.603179	+	1.85639i	−0.0943215	+	0.995542i	$0.530068\pi$
$499$	−13.4740	+	41.4687i	−0.603179	+	1.85639i	−0.508857	+	0.860851i	$0.669932\pi$
$500$	6.84209	−	9.41733i	0.305988	−	0.421156i
$501$	0.505056	−	0.695150i	0.0225643	−	0.0310570i
$502$	1.99504	−	6.14009i	0.0890429	−	0.274046i
$503$	−5.54672	−	17.0710i	−0.247316	−	0.761160i	−0.995247	−	0.0973838i	$-0.968953\pi$
$503$	−5.54672	−	17.0710i	−0.247316	−	0.761160i	0.747931	−	0.663777i	$-0.231047\pi$
$504$	−2.64515	+	0.0566111i	−0.117824	+	0.00252166i
$505$		−	27.7669i		−	1.23561i
$506$	−27.7446	−	5.25098i	−1.23340	−	0.233435i
$507$		−	3.05528i		−	0.135690i
$508$	−3.41815	−	4.70468i	−0.151656	−	0.208736i
$509$	9.80303	−	3.18520i	0.434512	−	0.141181i	−0.0835903	−	0.996500i	$-0.526639\pi$
$509$	9.80303	−	3.18520i	0.434512	−	0.141181i	0.518102	+	0.855319i	$0.326639\pi$
$510$	−6.43820	−	2.09190i	−0.285088	−	0.0926309i
$511$	−35.1223	+	12.2488i	−1.55372	+	0.541855i
$512$	0.587785	−	0.809017i	0.0259767	−	0.0357538i
$513$	−6.04736	−	1.96491i	−0.266998	−	0.0867528i
$514$	1.36534	+	4.20208i	0.0602225	+	0.185346i
$515$	6.73046	−	4.88996i	0.296579	−	0.215478i
$516$	−8.65762			−0.381131
$517$	2.37663	−	4.33792i	0.104524	−	0.190782i
$518$	−13.0790	−	9.08136i	−0.574660	−	0.399012i
$519$	1.88790	+	2.59847i	0.0828696	+	0.114060i
$520$	−1.46641	−	4.51314i	−0.0643062	−	0.197914i
$521$	12.1313	+	3.94170i	0.531482	+	0.172689i	0.562450	−	0.826831i	$-0.309859\pi$
$521$	12.1313	+	3.94170i	0.531482	+	0.172689i	−0.0309679	+	0.999520i	$0.509859\pi$
$522$	−0.693004	−	0.503497i	−0.0303320	−	0.0220375i
$523$	−11.3689	−	8.25995i	−0.497125	−	0.361183i	0.310793	−	0.950478i	$-0.399406\pi$
$523$	−11.3689	−	8.25995i	−0.497125	−	0.361183i	−0.807918	+	0.589295i	$0.799406\pi$
$524$	−4.80340	+	14.7833i	−0.209837	+	0.645813i
$525$	−2.08879	+	6.92978i	−0.0911621	+	0.302440i
$526$	−14.1731	+	10.2973i	−0.617975	+	0.448985i
$527$			28.2754i			1.23170i
$528$	2.99893	−	1.41649i	0.130511	−	0.0616448i
$529$	49.4851			2.15153
$530$	0.498530	−	0.362204i	0.0216548	−	0.0157331i
$531$	5.04243	−	1.63838i	0.218823	−	0.0710998i
$532$	10.1774	+	13.3956i	0.441246	+	0.580771i
$533$	25.7510	+	18.7092i	1.11540	+	0.810384i
$534$	−1.70513	+	2.34690i	−0.0737880	+	0.101560i
$535$	0.785480	−	2.41746i	0.0339593	−	0.104516i
$536$	−10.0209	+	3.25598i	−0.432836	+	0.140637i
$537$	9.68241	+	13.3267i	0.417827	+	0.575090i
$538$	21.3864			0.922033
$539$	10.8045	+	20.5490i	0.465383	+	0.885110i
$540$	1.50479			0.0647558
$541$	−8.98424	−	12.3658i	−0.386263	−	0.531645i	0.570967	−	0.820973i	$-0.306568\pi$
$541$	−8.98424	−	12.3658i	−0.386263	−	0.531645i	−0.957230	+	0.289328i	$0.906568\pi$
$542$	−22.6105	+	7.34658i	−0.971202	+	0.315563i
$543$	0.959007	−	2.95152i	0.0411549	−	0.126662i
$544$	−2.64424	+	3.63949i	−0.113371	+	0.156042i
$545$	−2.72009	−	1.97626i	−0.116516	−	0.0846537i
$546$	5.04746	+	6.64351i	0.216011	+	0.284316i
$547$	31.6740	−	10.2915i	1.35428	−	0.440034i	0.460153	−	0.887839i	$-0.347794\pi$
$547$	31.6740	−	10.2915i	1.35428	−	0.440034i	0.894131	+	0.447806i	$0.147794\pi$
$548$	−11.3520	+	8.24771i	−0.484933	+	0.352325i
$549$	7.17854			0.306373
$550$	−1.15017	−	8.99979i	−0.0490433	−	0.383752i
$551$			5.44675i			0.232040i
$552$	−6.88783	+	5.00430i	−0.293165	+	0.212997i
$553$	10.0014	−	33.1807i	0.425303	−	1.41099i
$554$	8.53277	−	26.2612i	0.362522	−	1.11573i
$555$	7.32658	+	5.32307i	0.310996	+	0.225952i
$556$	12.3341	+	8.96126i	0.523083	+	0.380042i
$557$	1.12265	+	0.364771i	0.0475681	+	0.0154558i	0.332704	−	0.943031i	$-0.392039\pi$
$557$	1.12265	+	0.364771i	0.0475681	+	0.0154558i	−0.285136	+	0.958487i	$0.592039\pi$
$558$	−1.94227	−	5.97769i	−0.0822228	−	0.253056i
$559$	16.0477	+	22.0878i	0.678747	+	0.934215i
$560$	−3.27027	−	2.27070i	−0.138194	−	0.0959544i
$561$	−13.4911	+	6.37230i	−0.569596	+	0.269039i
$562$	−5.10566			−0.215369
$563$	15.6267	−	11.3534i	0.658586	−	0.478491i	−0.207599	−	0.978214i	$-0.566565\pi$
$563$	15.6267	−	11.3534i	0.658586	−	0.478491i	0.866185	+	0.499723i	$0.166565\pi$
$564$	−0.460858	−	1.41837i	−0.0194056	−	0.0597244i
$565$	−15.1819	−	4.93290i	−0.638707	−	0.207528i
$566$	15.9953	−	22.0156i	0.672331	−	0.925385i
$567$	−2.49819	+	0.871235i	−0.104914	+	0.0365884i
$568$	13.6553	+	4.43688i	0.572964	+	0.186167i
$569$	17.7638	−	5.77182i	0.744699	−	0.241967i	0.0880003	−	0.996120i	$-0.471952\pi$
$569$	17.7638	−	5.77182i	0.744699	−	0.241967i	0.656699	+	0.754153i	$0.271952\pi$
$570$	−5.62412	−	7.74093i	−0.235568	−	0.324232i
$571$		−	14.5527i		−	0.609011i	−0.952511	−	0.304505i	$-0.901509\pi$
$571$		−	14.5527i		−	0.609011i	0.952511	−	0.304505i	$-0.0984912\pi$
$572$	−9.17262	−	5.02543i	−0.383527	−	0.210124i
$573$			12.3937i			0.517754i
$574$	26.6986	−	0.571401i	1.11438	−	0.0238498i
$575$	7.19715	+	22.1506i	0.300142	+	0.923742i
$576$	0.309017	−	0.951057i	0.0128757	−	0.0396274i
$577$	−8.04697	+	11.0757i	−0.335000	+	0.461088i	−0.942973	−	0.332870i	$-0.891983\pi$
$577$	−8.04697	+	11.0757i	−0.335000	+	0.461088i	0.607973	+	0.793958i	$0.291983\pi$
$578$	1.90318	−	2.61950i	0.0791619	−	0.108957i
$579$	4.96122	−	15.2691i	0.206181	−	0.634561i
$580$	−0.398324	−	1.22591i	−0.0165395	−	0.0509033i
$581$	0.145632	+	6.80462i	0.00604181	+	0.282303i
$582$		−	16.2012i		−	0.671561i
$583$	0.252566	−	1.33448i	0.0104602	−	0.0552686i
$584$		−	14.0591i		−	0.581771i
$585$	−2.78927	−	3.83910i	−0.115322	−	0.158727i
$586$	−8.18053	+	2.65801i	−0.337934	+	0.109802i
$587$	33.9781	+	11.0402i	1.40243	+	0.455676i	0.909975	−	0.414664i	$-0.136101\pi$
$587$	33.9781	+	11.0402i	1.40243	+	0.455676i	0.492452	+	0.870340i	$0.336101\pi$
$588$	6.74385	+	1.87631i	0.278112	+	0.0773776i
$589$	−23.4912	+	32.3329i	−0.967938	+	1.33225i
$590$	7.58779	+	2.46542i	0.312384	+	0.101500i
$591$	0.497139	+	1.53004i	0.0204496	+	0.0629373i
$592$	4.86884	−	3.53742i	0.200108	−	0.145387i
$593$	−8.32173			−0.341732			−0.170866	−	0.985294i	$-0.554657\pi$
$593$	−8.32173			−0.341732			−0.170866	+	0.985294i	$0.554657\pi$
$594$	2.41443	−	2.27388i	0.0990652	−	0.0932985i
$595$	14.7118	+	10.2151i	0.603126	+	0.418777i
$596$	−2.55934	−	3.52263i	−0.104835	−	0.144293i
$597$	−3.42961	−	10.5553i	−0.140365	−	0.431998i
$598$	25.5345	+	8.29666i	1.04418	+	0.339276i
$599$	15.3116	+	11.1245i	0.625615	+	0.454536i	0.854878	−	0.518829i	$-0.173632\pi$
$599$	15.3116	+	11.1245i	0.625615	+	0.454536i	−0.229264	+	0.973364i	$0.573632\pi$
$600$	−2.21315	−	1.60795i	−0.0903516	−	0.0656443i
$601$	5.45248	−	16.7810i	0.222411	−	0.684512i	−0.776133	−	0.630570i	$-0.782821\pi$
$601$	5.45248	−	16.7810i	0.222411	−	0.684512i	0.998544	−	0.0539421i	$-0.0171787\pi$
$602$	21.9313	+	6.61057i	0.893853	+	0.269427i
$603$	−8.52428	+	6.19325i	−0.347135	+	0.252209i
$604$			3.79187i			0.154289i
$605$	12.7845	+	10.5141i	0.519765	+	0.427460i
$606$	−18.4523			−0.749574
$607$	10.1576	−	7.37990i	0.412283	−	0.299541i	−0.362243	−	0.932084i	$-0.617989\pi$
$607$	10.1576	−	7.37990i	0.412283	−	0.299541i	0.774525	+	0.632543i	$0.217989\pi$
$608$	−6.04736	+	1.96491i	−0.245253	+	0.0796875i
$609$	1.37105	+	1.80459i	0.0555579	+	0.0731258i
$610$	8.73916	+	6.34937i	0.353838	+	0.257079i
$611$	−2.76439	+	3.80486i	−0.111835	+	0.153928i
$612$	−1.39016	+	4.27847i	−0.0561939	+	0.172947i
$613$	15.1401	−	4.91932i	0.611503	−	0.198689i	0.0131388	−	0.999914i	$-0.495818\pi$
$613$	15.1401	−	4.91932i	0.611503	−	0.198689i	0.598364	+	0.801224i	$0.295818\pi$
$614$	7.61589	+	10.4824i	0.307352	+	0.423034i
$615$	−15.1885			−0.612460
$616$	−8.67838	+	1.29838i	−0.349662	+	0.0523131i
$617$	−20.7236			−0.834303			−0.417151	−	0.908837i	$-0.636971\pi$
$617$	−20.7236			−0.834303			−0.417151	+	0.908837i	$0.636971\pi$
$618$	−3.24960	−	4.47269i	−0.130718	−	0.179918i
$619$	19.0574	−	6.19212i	0.765981	−	0.248882i	0.100137	−	0.994974i	$-0.468072\pi$
$619$	19.0574	−	6.19212i	0.765981	−	0.248882i	0.665844	+	0.746091i	$0.268072\pi$
$620$	2.92271	−	8.99516i	0.117379	−	0.361254i
$621$	−5.00430	+	6.88783i	−0.200816	+	0.276399i
$622$	−3.38552	−	2.45973i	−0.135747	−	0.0986260i
$623$	6.11137	−	4.64317i	0.244847	−	0.186025i
$624$	−2.99918	+	0.974493i	−0.120063	+	0.0390109i
$625$	3.10534	−	2.25616i	0.124214	−	0.0902465i
$626$	−6.47220			−0.258681
$627$	−20.7212	−	3.92171i	−0.827523	−	0.156618i
$628$			1.00386i			0.0400582i
$629$	−21.9032	+	15.9136i	−0.873339	+	0.634518i
$630$	−3.81190	−	1.14899i	−0.151870	−	0.0457768i
$631$	4.72632	−	14.5461i	0.188152	−	0.579072i	−0.811837	−	0.583885i	$-0.801532\pi$
$631$	4.72632	−	14.5461i	0.188152	−	0.579072i	0.999988	+	0.00481306i	$0.00153205\pi$
$632$	10.5969	+	7.69909i	0.421521	+	0.306253i
$633$	5.29012	+	3.84349i	0.210263	+	0.152765i
$634$	24.7982	+	8.05741i	0.984861	+	0.320001i
$635$	−2.70415	−	8.32252i	−0.107311	−	0.330269i
$636$	−0.240700	−	0.331296i	−0.00954439	−	0.0131367i
$637$	−7.71343	−	20.6832i	−0.305617	−	0.819498i
$638$	−2.49158	−	1.36507i	−0.0986427	−	0.0540436i
$639$	14.3580			0.567995
$640$	1.21740	−	0.884493i	0.0481220	−	0.0349627i
$641$	−8.46290	−	26.0461i	−0.334264	−	1.02876i	−0.967083	−	0.254460i	$-0.918102\pi$
$641$	−8.46290	−	26.0461i	−0.334264	−	1.02876i	0.632819	−	0.774300i	$-0.281898\pi$
$642$	−1.60651	−	0.521987i	−0.0634039	−	0.0206012i
$643$	−19.8778	+	27.3594i	−0.783904	+	1.07895i	0.210936	+	0.977500i	$0.432349\pi$
$643$	−19.8778	+	27.3594i	−0.783904	+	1.07895i	−0.994840	+	0.101452i	$0.967651\pi$
$644$	21.2691	−	7.41754i	0.838121	−	0.292292i
$645$	−12.3903	−	4.02584i	−0.487867	−	0.158517i
$646$	27.2050	−	8.83944i	1.07037	−	0.347783i
$647$	−4.26619	−	5.87191i	−0.167721	−	0.230849i	0.716880	−	0.697196i	$-0.245569\pi$
$647$	−4.26619	−	5.87191i	−0.167721	−	0.230849i	−0.884601	+	0.466348i	$0.845569\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	15.9001	−	7.51012i	0.624132	−	0.294798i
$650$			8.62681i			0.338371i
$651$	0.355818	+	16.6256i	0.0139456	+	0.651607i
$652$	−2.33647	−	7.19090i	−0.0915030	−	0.281617i
$653$	0.580596	−	1.78689i	0.0227205	−	0.0699265i	−0.939053	−	0.343771i	$-0.888295\pi$
$653$	0.580596	−	1.78689i	0.0227205	−	0.0699265i	0.961774	+	0.273845i	$0.0882955\pi$
$654$	−1.31331	+	1.80762i	−0.0513546	+	0.0706836i
$655$	−13.7487	+	18.9234i	−0.537205	+	0.739399i
$656$	−3.11905	+	9.59944i	−0.121778	+	0.374795i
$657$	−4.34451	−	13.3710i	−0.169495	−	0.521653i
$658$	0.0844279	+	3.94488i	0.00329134	+	0.153788i
$659$			42.0498i			1.63803i	0.573773	+	0.819014i	$0.305479\pi$
$659$			42.0498i			1.63803i	−0.573773	+	0.819014i	$0.694521\pi$
$660$	4.95056	−	0.632679i	0.192700	−	0.0246270i
$661$			0.465429i			0.0181031i	0.999959	+	0.00905155i	$0.00288124\pi$
$661$			0.465429i			0.0181031i	−0.999959	+	0.00905155i	$0.997119\pi$
$662$	−6.99350	−	9.62573i	−0.271810	−	0.374115i
$663$	13.4923	−	4.38391i	0.523997	−	0.170257i
$664$	−2.44659	−	0.794944i	−0.0949459	−	0.0308498i
$665$	8.33626	+	23.9035i	0.323266	+	0.926937i
$666$	3.53742	−	4.86884i	0.137072	−	0.188664i
$667$	6.93600	+	2.25364i	0.268563	+	0.0872614i
$668$	−0.265524	−	0.817198i	−0.0102734	−	0.0316184i
$669$	3.20297	−	2.32709i	0.123834	−	0.0899706i
$670$	−15.8553			−0.612545
$671$	23.6165	−	3.01817i	0.911703	−	0.116515i
$672$	−1.50898	+	2.17324i	−0.0582101	+	0.0838347i
$673$	1.99982	+	2.75252i	0.0770876	+	0.106102i	0.845820	−	0.533469i	$-0.179112\pi$
$673$	1.99982	+	2.75252i	0.0770876	+	0.106102i	−0.768732	+	0.639571i	$0.779112\pi$
$674$	3.18973	+	9.81697i	0.122864	+	0.378136i
$675$	−2.60172	−	0.845349i	−0.100140	−	0.0325375i
$676$	−2.47177	−	1.79585i	−0.0950682	−	0.0690711i
$677$	0.0647986	+	0.0470789i	0.00249041	+	0.00180939i	0.589030	−	0.808111i	$-0.299510\pi$
$677$	0.0647986	+	0.0470789i	0.00249041	+	0.00180939i	−0.586539	+	0.809921i	$0.699510\pi$
$678$	−3.27813	+	10.0890i	−0.125896	+	0.387467i
$679$	−12.3705	+	41.0405i	−0.474736	+	1.57499i
$680$	−5.47666	+	3.97903i	−0.210020	+	0.152589i
$681$			8.84589i			0.338975i
$682$	−8.90308	−	18.8492i	−0.340917	−	0.721773i
$683$	12.4235			0.475373			0.237687	−	0.971342i	$-0.423611\pi$
$683$	12.4235			0.475373			0.237687	+	0.971342i	$0.423611\pi$
$684$	−5.14420	+	3.73748i	−0.196693	+	0.142906i
$685$	−20.0815	+	6.52489i	−0.767276	+	0.249303i
$686$	−15.6507	−	9.90231i	−0.597546	−	0.378072i
$687$	−19.3849	−	14.0839i	−0.739580	−	0.537336i
$688$	−5.08882	+	7.00417i	−0.194010	+	0.267031i
$689$	−0.399059	+	1.22818i	−0.0152029	+	0.0467898i
$690$	−12.1845	+	3.95897i	−0.463855	+	0.150716i
$691$	−18.7038	−	25.7436i	−0.711526	−	0.979332i	−0.999763	−	0.0217729i	$-0.993069\pi$
$691$	−18.7038	−	25.7436i	−0.711526	−	0.979332i	0.288236	−	0.957559i	$-0.406931\pi$
$692$	3.21189			0.122098
$693$	−7.85241	+	3.91660i	−0.298288	+	0.148779i
$694$	−13.3470			−0.506646
$695$	13.4848	+	18.5603i	0.511508	+	0.704030i
$696$	−0.814675	+	0.264704i	−0.0308802	+	0.0100336i
$697$	14.0315	−	43.1845i	0.531481	−	1.63573i
$698$	−4.95041	+	6.81366i	−0.187376	+	0.257901i
$699$	10.9159	+	7.93086i	0.412877	+	0.299973i
$700$	4.37855	+	5.76308i	0.165494	+	0.217824i
$701$	−10.2780	+	3.33954i	−0.388196	+	0.126133i	−0.496611	−	0.867973i	$-0.665423\pi$
$701$	−10.2780	+	3.33954i	−0.388196	+	0.126133i	0.108415	+	0.994106i	$0.465423\pi$
$702$	−2.55126	+	1.85360i	−0.0962909	+	0.0699595i
$703$	−38.2673			−1.44328
$704$	0.616760	−	3.25877i	0.0232450	−	0.122820i
$705$		−	2.24419i		−	0.0845213i
$706$	−12.4007	+	9.00961i	−0.466705	+	0.339081i
$707$	46.7430	+	14.0894i	1.75795	+	0.529885i
$708$	1.63838	−	5.04243i	0.0615742	−	0.189506i
$709$	−19.1290	−	13.8980i	−0.718404	−	0.521951i	0.167470	−	0.985877i	$-0.446440\pi$
$709$	−19.1290	−	13.8980i	−0.718404	−	0.521951i	−0.885874	+	0.463926i	$0.846440\pi$
$710$	17.4795	+	12.6996i	0.655994	+	0.476607i
$711$	12.4574	+	4.04765i	0.467188	+	0.151799i
$712$	0.896437	+	2.75895i	0.0335954	+	0.103396i
$713$	31.4536	+	43.2921i	1.17795	+	1.62130i
$714$	6.78837	−	9.77667i	0.254048	−	0.365883i
$715$	−10.7905	−	11.4574i	−0.403540	−	0.428483i
$716$	16.4727			0.615614
$717$	−17.1258	+	12.4426i	−0.639575	+	0.464679i
$718$	7.92322	+	24.3852i	0.295692	+	0.910046i
$719$	−47.9805	−	15.5898i	−1.78937	−	0.581402i	−0.789880	−	0.613261i	$-0.789857\pi$
$719$	−47.9805	−	15.5898i	−1.78937	−	0.581402i	−0.999492	+	0.0318591i	$0.989857\pi$
$720$	0.884493	−	1.21740i	0.0329631	−	0.0453698i
$721$	4.81667	+	13.8114i	0.179382	+	0.514362i
$722$	20.3825	+	6.62269i	0.758560	+	0.246471i
$723$	−6.25920	+	2.03374i	−0.232782	+	0.0756355i
$724$	−1.82414	−	2.51071i	−0.0677936	−	0.0933099i
$725$			2.34332i			0.0870288i
$726$	6.98711	−	8.49590i	0.259316	−	0.315312i
$727$			20.3701i			0.755487i	0.925910	+	0.377743i	$0.123300\pi$
$727$			20.3701i			0.755487i	−0.925910	+	0.377743i	$0.876700\pi$
$728$	8.34153	−	0.178524i	0.309158	−	0.00661655i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	6.53757	−	20.1206i	0.241966	−	0.744696i
$731$	22.8929	−	31.5093i	0.846723	−	1.16541i
$732$	4.21944	−	5.80756i	0.155955	−	0.214654i
$733$	−6.18623	+	19.0392i	−0.228493	+	0.703231i	0.769425	+	0.638738i	$0.220543\pi$
$733$	−6.18623	+	19.0392i	−0.228493	+	0.703231i	−0.997918	+	0.0644931i	$0.979457\pi$
$734$	1.65859	+	5.10461i	0.0612196	+	0.188415i
$735$	8.77890	+	5.82119i	0.323814	+	0.214718i
$736$			8.51382i			0.313824i
$737$	−25.4398	+	23.9589i	−0.937088	+	0.882539i
$738$			10.0934i			0.371545i
$739$	−17.8090	−	24.5120i	−0.655116	−	0.901690i	0.344192	−	0.938899i	$-0.388153\pi$
$739$	−17.8090	−	24.5120i	−0.655116	−	0.901690i	−0.999307	+	0.0372097i	$0.988153\pi$
$740$	8.61291	−	2.79851i	0.316617	−	0.102875i
$741$	19.0705	+	6.19639i	0.700573	+	0.227630i
$742$	0.356774	+	1.02302i	0.0130976	+	0.0375562i
$743$	21.6213	−	29.7592i	0.793210	−	1.09176i	−0.200491	−	0.979695i	$-0.564254\pi$
$743$	21.6213	−	29.7592i	0.793210	−	1.09176i	0.993701	−	0.112064i	$-0.0357461\pi$
$744$	−5.97769	−	1.94227i	−0.219153	−	0.0712070i
$745$	−2.02473	−	6.23148i	−0.0741804	−	0.228304i
$746$	21.6196	−	15.7076i	0.791550	−	0.575094i
$747$	−2.57249			−0.0941226
$748$	−2.77459	+	14.6601i	−0.101449	+	0.536026i
$749$	3.67101	+	2.54894i	0.134136	+	0.0931363i
$750$	−6.84209	−	9.41733i	−0.249838	−	0.343872i
$751$	−5.14598	−	15.8377i	−0.187780	−	0.577926i	0.812206	−	0.583371i	$-0.198267\pi$
$751$	−5.14598	−	15.8377i	−0.187780	−	0.577926i	−0.999985	+	0.00544509i	$0.998267\pi$
$752$	−1.41837	−	0.460858i	−0.0517228	−	0.0168058i
$753$	−5.22307	−	3.79479i	−0.190339	−	0.138290i
$754$	2.18541	+	1.58779i	0.0795878	+	0.0578239i
$755$	−1.76324	+	5.42669i	−0.0641708	+	0.197498i
$756$	−0.763555	+	2.53318i	−0.0277702	+	0.0921307i
$757$	23.7142	−	17.2294i	0.861908	−	0.626212i	−0.0664957	−	0.997787i	$-0.521182\pi$
$757$	23.7142	−	17.2294i	0.861908	−	0.626212i	0.928403	+	0.371574i	$0.121182\pi$
$758$			16.5349i			0.600573i
$759$	−13.5675	+	24.7641i	−0.492470	+	0.898878i
$760$	−9.56832			−0.347079
$761$	27.4324	−	19.9308i	0.994424	−	0.722492i	0.0335388	−	0.999437i	$-0.489322\pi$
$761$	27.4324	−	19.9308i	0.994424	−	0.722492i	0.960886	+	0.276946i	$0.0893223\pi$
$762$	−5.53068	+	1.79703i	−0.200356	+	0.0650995i
$763$	4.70707	−	3.57624i	0.170407	−	0.129468i
$764$	10.0267	+	7.28483i	0.362754	+	0.263556i
$765$	−3.97903	+	5.47666i	−0.143862	+	0.198009i
$766$	−8.83706	+	27.1977i	−0.319296	+	0.982692i
$767$	−15.9014	+	5.16668i	−0.574167	+	0.186558i
$768$	−0.587785	−	0.809017i	−0.0212099	−	0.0291929i
$769$	−26.0342			−0.938816			−0.469408	−	0.882981i	$-0.655533\pi$
$769$	−26.0342			−0.938816			−0.469408	+	0.882981i	$0.655533\pi$
$770$	−13.0237	−	2.17733i	−0.469342	−	0.0784657i
$771$	4.41833			0.159122
$772$	−9.43680	−	12.9886i	−0.339638	−	0.467471i
$773$	26.4105	−	8.58128i	0.949919	−	0.308647i	0.207236	−	0.978291i	$-0.433553\pi$
$773$	26.4105	−	8.58128i	0.949919	−	0.308647i	0.742682	+	0.669644i	$0.233553\pi$
$774$	−2.67535	+	8.23389i	−0.0961636	+	0.295961i
$775$	−10.1065	+	13.9104i	−0.363035	+	0.499675i
$776$	−13.1070	−	9.52282i	−0.470515	−	0.341849i
$777$	−12.6785	+	9.63262i	−0.454840	+	0.345568i
$778$	−6.88657	+	2.23758i	−0.246895	+	0.0802212i
$779$	51.9227	−	37.7240i	1.86032	−	1.35160i
$780$	−4.74539			−0.169912
$781$	47.2361	−	6.03674i	1.69024	−	0.216012i
$782$		−	38.3007i		−	1.36963i
$783$	−0.693004	+	0.503497i	−0.0247659	+	0.0179935i
$784$	5.48190	−	4.35302i	0.195782	−	0.155465i
$785$	−0.466799	+	1.43666i	−0.0166608	+	0.0512766i
$786$	12.5755	+	9.13660i	0.448552	+	0.325892i
$787$	4.23522	+	3.07707i	0.150969	+	0.109686i	0.660706	−	0.750645i	$-0.270257\pi$
$787$	4.23522	+	3.07707i	0.150969	+	0.109686i	−0.509736	+	0.860331i	$0.670257\pi$
$788$	1.53004	+	0.497139i	0.0545053	+	0.0177099i
$789$	5.41363	+	16.6614i	0.192730	+	0.593163i
$790$	11.5855	+	15.9461i	0.412194	+	0.567336i
$791$	16.0076	−	23.0543i	0.569165	−	0.819717i
$792$	−0.420443	−	3.28987i	−0.0149398	−	0.116900i
$793$	−22.6377			−0.803889
$794$	−6.24819	+	4.53958i	−0.221740	+	0.161104i
$795$	−0.190422	−	0.586058i	−0.00675356	−	0.0207853i
$796$	−10.5553	−	3.42961i	−0.374121	−	0.121559i
$797$	7.31134	−	10.0632i	0.258981	−	0.356457i	−0.659650	−	0.751573i	$-0.729296\pi$
$797$	7.31134	−	10.0632i	0.258981	−	0.356457i	0.918631	+	0.395116i	$0.129296\pi$
$798$	15.8849	−	5.53981i	0.562320	−	0.196107i
$799$	6.38078	+	2.07324i	0.225736	+	0.0733460i
$800$	−2.60172	+	0.845349i	−0.0919846	+	0.0298876i
$801$	1.70513	+	2.34690i	0.0602476	+	0.0829238i
$802$		−	15.6285i		−	0.551862i
$803$	−19.9146	−	42.1623i	−0.702771	−	1.48787i
$804$			10.5366i			0.371597i
$805$	33.8883	−	0.725273i	1.19441	−	0.0255625i
$806$	6.12499	+	18.8508i	0.215744	+	0.663991i
$807$	6.60876	−	20.3397i	0.232639	−	0.715991i
$808$	−10.8460	+	14.9282i	−0.381561	+	0.525174i
$809$	−6.11002	+	8.40972i	−0.214817	+	0.295670i	−0.902804	−	0.430053i	$-0.858495\pi$
$809$	−6.11002	+	8.40972i	−0.214817	+	0.295670i	0.687987	+	0.725723i	$0.258495\pi$
$810$	0.465006	−	1.43114i	0.0163386	−	0.0502851i
$811$	−14.6027	−	44.9426i	−0.512771	−	1.57815i	−0.787301	−	0.616568i	$-0.788522\pi$
$811$	−14.6027	−	44.9426i	−0.512771	−	1.57815i	0.274530	−	0.961578i	$-0.411478\pi$
$812$	2.26583	−	0.0484930i	0.0795151	−	0.00170177i
$813$			23.7740i			0.833792i
$814$	9.59057	−	17.5051i	0.336149	−	0.613554i
$815$		−	11.3777i		−	0.398542i
$816$	2.64424	+	3.63949i	0.0925670	+	0.127408i
$817$	52.3558	−	17.0114i	1.83170	−	0.595155i
$818$	20.9421	+	6.80449i	0.732222	+	0.237913i
$819$	7.87810	−	2.74746i	0.275283	−	0.0960041i
$820$	−8.92758	+	12.2878i	−0.311765	+	0.429107i
$821$	21.8900	+	7.11250i	0.763967	+	0.248228i	0.664980	−	0.746861i	$-0.268440\pi$
$821$	21.8900	+	7.11250i	0.763967	+	0.248228i	0.0989865	+	0.995089i	$0.468440\pi$
$822$	4.33608	+	13.3451i	0.151238	+	0.465463i
$823$	−34.8600	+	25.3272i	−1.21514	+	0.882852i	−0.995688	−	0.0927705i	$-0.970428\pi$
$823$	−34.8600	+	25.3272i	−1.21514	+	0.882852i	−0.219454	+	0.975623i	$0.570428\pi$
$824$	−5.52855			−0.192596
$825$	−8.91473	−	1.68721i	−0.310371	−	0.0587412i
$826$	−8.00048	+	11.5224i	−0.278372	+	0.400914i
$827$	−19.8279	−	27.2908i	−0.689484	−	0.948993i	0.310515	−	0.950569i	$-0.399499\pi$
$827$	−19.8279	−	27.2908i	−0.689484	−	0.948993i	−0.999999	+	0.00157512i	$0.999499\pi$
$828$	2.63092	+	8.09712i	0.0914306	+	0.281395i
$829$	21.4996	+	6.98563i	0.746711	+	0.242621i	0.657565	−	0.753398i	$-0.271586\pi$
$829$	21.4996	+	6.98563i	0.746711	+	0.242621i	0.0891456	+	0.996019i	$0.471586\pi$
$830$	−3.13175	−	2.27535i	−0.108705	−	0.0789786i
$831$	−22.3391	−	16.2303i	−0.774934	−	0.563022i
$832$	−0.974493	+	2.99918i	−0.0337845	+	0.103978i
$833$	−24.6612	+	19.5827i	−0.854459	+	0.678501i
$834$	12.3341	−	8.96126i	0.427095	−	0.310303i
$835$		−	1.29300i		−	0.0447460i
$836$	−15.3523	+	14.4586i	−0.530971	+	0.500063i
$837$	−6.28531			−0.217252
$838$	24.5702	−	17.8513i	0.848764	−	0.616663i
$839$	−21.0986	+	6.85534i	−0.728404	+	0.236673i	−0.649663	−	0.760222i	$-0.725090\pi$
$839$	−21.0986	+	6.85534i	−0.728404	+	0.236673i	−0.0787408	+	0.996895i	$0.525090\pi$
$840$	−3.17013	+	2.40853i	−0.109380	+	0.0831022i
$841$	−22.8679	−	16.6145i	−0.788547	−	0.572913i
$842$	−14.8883	+	20.4920i	−0.513084	+	0.706200i
$843$	−1.57774	+	4.85577i	−0.0543401	+	0.167242i
$844$	6.21891	−	2.02064i	0.214064	−	0.0695535i
$845$	−2.70237	−	3.71950i	−0.0929645	−	0.127955i
$846$	−1.49137			−0.0512743
$847$	−24.1867	+	16.1866i	−0.831064	+	0.556177i
$848$	−0.409504			−0.0140624
$849$	−15.9953	−	22.0156i	−0.548956	−	0.755573i
$850$	11.7042	−	3.80293i	0.401452	−	0.130440i
$851$	−15.8334	+	48.7303i	−0.542763	+	1.67045i
$852$	8.43945	−	11.6159i	0.289131	−	0.397954i
$853$	−32.6636	−	23.7315i	−1.11838	−	0.812550i	−0.134417	−	0.990925i	$-0.542916\pi$
$853$	−32.6636	−	23.7315i	−1.11838	−	0.812550i	−0.983963	+	0.178375i	$0.942916\pi$
$854$	−15.1230	+	11.4898i	−0.517498	+	0.393173i
$855$	−9.10001	+	2.95677i	−0.311214	+	0.101120i
$856$	−1.36658	+	0.992877i	−0.0467087	+	0.0339359i
$857$	20.2644			0.692218			0.346109	−	0.938194i	$-0.387503\pi$
$857$	20.2644			0.692218			0.346109	+	0.938194i	$0.387503\pi$
$858$	−7.61396	+	7.17074i	−0.259936	+	0.244805i
$859$			13.1327i			0.448082i	0.974580	+	0.224041i	$0.0719250\pi$
$859$			13.1327i			0.448082i	−0.974580	+	0.224041i	$0.928075\pi$
$860$	−10.5398	+	7.65761i	−0.359404	+	0.261122i
$861$	7.70690	−	25.5685i	0.262650	−	0.871372i
$862$	−1.00226	+	3.08465i	−0.0341372	+	0.105064i
$863$	−11.8874	−	8.63669i	−0.404651	−	0.293996i	0.366781	−	0.930307i	$-0.380460\pi$
$863$	−11.8874	−	8.63669i	−0.404651	−	0.293996i	−0.771433	+	0.636311i	$0.780460\pi$
$864$	−0.809017	−	0.587785i	−0.0275233	−	0.0199969i
$865$	4.59666	+	1.49354i	0.156291	+	0.0507820i
$866$	−9.40139	−	28.9345i	−0.319472	−	0.983235i
$867$	−1.90318	−	2.61950i	−0.0646354	−	0.0889630i
$868$	13.6595	+	9.48440i	0.463634	+	0.321921i
$869$	42.6849	+	8.07861i	1.44799	+	0.274048i
$870$	−1.28900			−0.0437013
$871$	26.8815	−	19.5306i	0.910846	−	0.661768i
$872$	0.690450	+	2.12499i	0.0233816	+	0.0719611i
$873$	−15.4083	−	5.00644i	−0.521490	−	0.169442i
$874$	31.8202	−	43.7968i	1.07633	−	1.48145i
$875$	10.1416	+	29.0801i	0.342848	+	0.983086i
$876$	−13.3710	−	4.34451i	−0.451765	−	0.146787i
$877$	20.0863	−	6.52643i	0.678266	−	0.220382i	0.0504300	−	0.998728i	$-0.483941\pi$
$877$	20.0863	−	6.52643i	0.678266	−	0.220382i	0.627836	+	0.778346i	$0.283941\pi$
$878$	7.14306	+	9.83157i	0.241066	+	0.331800i
$879$			8.60151i			0.290122i
$880$	2.39802	−	4.37697i	0.0808372	−	0.147547i
$881$		−	24.8273i		−	0.836453i	−0.908343	−	0.418226i	$-0.862652\pi$
$881$		−	24.8273i		−	0.836453i	0.908343	−	0.418226i	$-0.137348\pi$
$882$	3.86844	−	5.83397i	0.130257	−	0.196440i
$883$	−0.850830	−	2.61859i	−0.0286327	−	0.0881224i	0.935719	−	0.352746i	$-0.114752\pi$
$883$	−0.850830	−	2.61859i	−0.0286327	−	0.0881224i	−0.964352	+	0.264624i	$0.914752\pi$
$884$	4.38391	−	13.4923i	0.147447	−	0.453794i
$885$	4.68951	−	6.45456i	0.157636	−	0.216968i
$886$	−4.46978	+	6.15213i	−0.150165	+	0.206685i
$887$	−3.23286	+	9.94972i	−0.108549	+	0.334079i	−0.990547	−	0.137174i	$-0.956198\pi$
$887$	−3.23286	+	9.94972i	−0.108549	+	0.334079i	0.881998	+	0.471253i	$0.156198\pi$
$888$	−1.85973	−	5.72367i	−0.0624085	−	0.192074i
$889$	15.3823	−	0.329211i	0.515907	−	0.0110414i
$890$			4.36529i			0.146325i
$891$	−1.41649	−	2.99893i	−0.0474542	−	0.100468i
$892$		−	3.95909i		−	0.132560i
$893$	5.57395	+	7.67189i	0.186525	+	0.256730i
$894$	−4.14110	+	1.34552i	−0.138499	+	0.0450011i
$895$	23.5748	+	7.65990i	0.788017	+	0.256042i
$896$	0.871235	+	2.49819i	0.0291059	+	0.0834586i
$897$	15.7812	−	21.7209i	0.526918	−	0.725241i
$898$	−6.93261	−	2.25254i	−0.231344	−	0.0751683i
$899$	1.66375	+	5.12049i	0.0554891	+	0.170778i
$900$	−2.21315	+	1.60795i	−0.0737718	+	0.0535983i
$901$	1.84222			0.0613731
$902$	4.24372	+	33.2061i	0.141300	+	1.10564i
$903$	13.0642	−	18.8151i	0.434748	−	0.626128i
$904$	6.23537	+	8.58225i	0.207385	+	0.285442i
$905$	−1.44310	−	4.44142i	−0.0479704	−	0.147638i
$906$	3.60628	+	1.17175i	0.119811	+	0.0389288i
$907$	−19.3498	−	14.0584i	−0.642499	−	0.466803i	0.218209	−	0.975902i	$-0.429979\pi$
$907$	−19.3498	−	14.0584i	−0.642499	−	0.466803i	−0.860708	+	0.509099i	$0.829979\pi$
$908$	7.15647	+	5.19948i	0.237496	+	0.172551i
$909$	−5.70208	+	17.5492i	−0.189126	+	0.582070i
$910$	12.0209	+	3.62337i	0.398490	+	0.120113i
$911$	14.6111	−	10.6156i	0.484087	−	0.351710i	−0.318819	−	0.947816i	$-0.603286\pi$
$911$	14.6111	−	10.6156i	0.484087	−	0.351710i	0.802906	+	0.596106i	$0.203286\pi$
$912$			6.35857i			0.210553i
$913$	−8.46316	+	1.08159i	−0.280090	+	0.0357953i
$914$	−11.8554			−0.392143
$915$	8.73916	−	6.34937i	0.288908	−	0.209904i
$916$	−22.7883	+	7.40437i	−0.752947	+	0.244647i
$917$	−24.8795	−	32.7467i	−0.821595	−	1.08139i
$918$	3.63949	+	2.64424i	0.120121	+	0.0872730i
$919$	−33.0979	+	45.5554i	−1.09180	+	1.50273i	−0.245973	+	0.969277i	$0.579108\pi$
$919$	−33.0979	+	45.5554i	−1.09180	+	1.50273i	−0.845827	+	0.533458i	$0.820892\pi$
$920$	−3.95897	+	12.1845i	−0.130524	+	0.401710i
$921$	12.3228	−	4.00391i	0.406049	−	0.131933i
$922$	17.4822	+	24.0622i	0.575747	+	0.792447i
$923$	−45.2785			−1.49036
$924$	−1.44694	+	8.65485i	−0.0476007	+	0.284724i
$925$	−16.4635			−0.541316
$926$	13.0037	+	17.8981i	0.427328	+	0.588167i
$927$	−5.25796	+	1.70842i	−0.172694	+	0.0561117i
$928$	−0.264704	+	0.814675i	−0.00868933	+	0.0267430i
$929$	21.3229	−	29.3485i	0.699583	−	0.962893i	−0.300376	−	0.953821i	$-0.597112\pi$
$929$	21.3229	−	29.3485i	0.699583	−	0.962893i	0.999959	−	0.00907229i	$-0.00288784\pi$
$930$	−7.65174	−	5.55932i	−0.250910	−	0.182297i
$931$	−44.4693	+	1.90432i	−1.45742	+	0.0624117i
$932$	12.8324	−	4.16950i	0.420339	−	0.136576i
$933$	−3.38552	+	2.45973i	−0.110837	+	0.0805278i
$934$	−39.8738			−1.30471
$935$	−10.7879	+	19.6905i	−0.352800	+	0.643947i
$936$			3.15352i			0.103076i
$937$	5.27546	−	3.83285i	0.172342	−	0.125214i	−0.498271	−	0.867022i	$-0.666031\pi$
$937$	5.27546	−	3.83285i	0.172342	−	0.125214i	0.670612	+	0.741808i	$0.266031\pi$
$938$	8.04526	−	26.6910i	0.262687	−	0.871493i
$939$	−2.00002	+	6.15543i	−0.0652682	+	0.200875i
$940$	−1.81559	−	1.31910i	−0.0592181	−	0.0430244i
$941$	−17.4047	−	12.6453i	−0.567377	−	0.412224i	0.266774	−	0.963759i	$-0.414042\pi$
$941$	−17.4047	−	12.6453i	−0.567377	−	0.412224i	−0.834151	+	0.551535i	$0.814042\pi$
$942$	0.954725	+	0.310209i	0.0311066	+	0.0101071i
$943$	−26.5550	−	81.7279i	−0.864750	−	2.66143i
$944$	−3.11639	−	4.28934i	−0.101430	−	0.139606i
$945$	−2.27070	+	3.27027i	−0.0738657	+	0.106382i
$946$	−5.33967	+	28.2132i	−0.173608	+	0.917292i
$947$	3.45408			0.112243			0.0561213	−	0.998424i	$-0.482127\pi$
$947$	3.45408			0.112243			0.0561213	+	0.998424i	$0.482127\pi$
$948$	10.5969	−	7.69909i	0.344171	−	0.250055i
$949$	13.7005	+	42.1658i	0.444737	+	1.36876i
$950$	16.5432	+	5.37522i	0.536733	+	0.174395i
$951$	15.3261	−	21.0946i	0.496983	−	0.684039i
$952$	−3.91939	−	11.2385i	−0.127028	−	0.364241i
$953$	−22.1944	−	7.21138i	−0.718946	−	0.233600i	−0.0733796	−	0.997304i	$-0.523378\pi$
$953$	−22.1944	−	7.21138i	−0.718946	−	0.233600i	−0.645566	+	0.763704i	$0.723378\pi$
$954$	−0.389461	+	0.126544i	−0.0126093	+	0.00409700i
$955$	10.9621	+	15.0881i	0.354727	+	0.488239i
$956$			21.1687i			0.684644i
$957$	−2.06820	+	1.94781i	−0.0668554	+	0.0629636i
$958$			39.2735i			1.26887i
$959$	−0.794358	−	37.1163i	−0.0256511	−	1.19855i
$960$	−0.465006	−	1.43114i	−0.0150080	−	0.0461898i
$961$	−2.62823	+	8.08887i	−0.0847817	+	0.260931i
$962$	−11.1553	+	15.3540i	−0.359663	+	0.495033i
$963$	−0.992877	+	1.36658i	−0.0319950	+	0.0440374i
$964$	−2.03374	+	6.25920i	−0.0655023	+	0.201595i
$965$	−7.46559	−	22.9767i	−0.240326	−	0.739647i
$966$	−0.481976	−	22.5203i	−0.0155073	−	0.724579i
$967$		−	3.04561i		−	0.0979402i	−0.998800	−	0.0489701i	$-0.984406\pi$
$967$		−	3.04561i		−	0.0979402i	0.998800	−	0.0489701i	$-0.0155939\pi$
$968$	−2.76641	−	10.6465i	−0.0889156	−	0.342190i
$969$		−	28.6050i		−	0.918926i
$970$	−14.3298	−	19.7233i	−0.460104	−	0.633278i
$971$	−44.8045	+	14.5579i	−1.43784	+	0.467184i	−0.921225	−	0.389031i	$-0.872810\pi$
$971$	−44.8045	+	14.5579i	−1.43784	+	0.467184i	−0.516620	+	0.856215i	$0.672810\pi$
$972$	−0.951057	−	0.309017i	−0.0305052	−	0.00991172i
$973$	−38.0869	+	13.2827i	−1.22101	+	0.425823i
$974$	−1.70537	+	2.34724i	−0.0546436	+	0.0752105i
$975$	8.20458	+	2.66583i	0.262757	+	0.0853749i
$976$	−2.21829	−	6.82720i	−0.0710058	−	0.218533i
$977$	1.36246	−	0.989886i	0.0435890	−	0.0316693i	−0.565777	−	0.824558i	$-0.691424\pi$
$977$	1.36246	−	0.989886i	0.0435890	−	0.0316693i	0.609366	+	0.792889i	$0.291424\pi$
$978$	−7.56096			−0.241773
$979$	6.59638	+	7.00409i	0.210821	+	0.223852i
$980$	9.86954	−	3.68067i	0.315271	−	0.117575i
$981$	1.31331	+	1.80762i	0.0419309	+	0.0577129i
$982$	−2.13038	−	6.55664i	−0.0679833	−	0.209231i
$983$	−2.81043	−	0.913165i	−0.0896389	−	0.0291254i	0.263854	−	0.964563i	$-0.415006\pi$
$983$	−2.81043	−	0.913165i	−0.0896389	−	0.0291254i	−0.353493	+	0.935437i	$0.615006\pi$
$984$	8.16577	+	5.93278i	0.260315	+	0.189130i
$985$	1.95853	+	1.42295i	0.0624038	+	0.0453390i
$986$	1.19081	−	3.66494i	0.0379232	−	0.116715i
$987$	3.77790	+	1.13874i	0.120252	+	0.0362465i
$988$	16.2223	−	11.7862i	0.516102	−	0.374970i
$989$		−	73.7095i		−	2.34382i
$990$	0.928094	−	4.90377i	0.0294967	−	0.155852i
$991$	18.7896			0.596873			0.298436	−	0.954430i	$-0.403535\pi$
$991$	18.7896			0.596873			0.298436	+	0.954430i	$0.403535\pi$
$992$	−5.08492	+	3.69441i	−0.161447	+	0.117298i
$993$	−11.3157	+	3.67670i	−0.359094	+	0.116677i
$994$	−30.2480	+	22.9812i	−0.959408	+	0.728918i
$995$	−13.5113	−	9.81651i	−0.428336	−	0.311204i
$996$	−1.51207	+	2.08119i	−0.0479119	+	0.0659450i
$997$	9.83743	−	30.2765i	0.311555	−	0.958866i	−0.665595	−	0.746313i	$-0.731822\pi$
$997$	9.83743	−	30.2765i	0.311555	−	0.958866i	0.977150	−	0.212553i	$-0.0681779\pi$
$998$	41.4687	−	13.4740i	1.31267	−	0.426512i
$999$	−3.53742	−	4.86884i	−0.111919	−	0.154043i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.u.a.349.2	yes	32
7.6	odd	2		462.2.u.b.349.3	yes	32
11.7	odd	10		462.2.u.b.139.3	yes	32
77.62	even	10	inner	462.2.u.a.139.2	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.u.a.139.2	✓	32	77.62	even	10	inner
462.2.u.a.349.2	yes	32	1.1	even	1	trivial
462.2.u.b.139.3	yes	32	11.7	odd	10
462.2.u.b.349.3	yes	32	7.6	odd	2

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.u (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.884493 + 1.21740i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-1.60058 - 2.10669i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.587785 - 0.809017i) q^{2} +(-0.951057 + 0.309017i) q^{3} +(-0.309017 + 0.951057i) q^{4} +(-0.884493 + 1.21740i) q^{5} +(0.809017 + 0.587785i) q^{6} +(-1.60058 - 2.10669i) q^{7} +(0.951057 - 0.309017i) q^{8} +(0.809017 - 0.587785i) q^{9} +1.50479 q^{10} +(2.41443 - 2.27388i) q^{11} -1.00000i q^{12} +(-2.55126 + 1.85360i) q^{13} +(-0.763555 + 2.53318i) q^{14} +(0.465006 - 1.43114i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(3.63949 + 2.64424i) q^{17} +(-0.951057 - 0.309017i) q^{18} +(1.96491 + 6.04736i) q^{19} +(-0.884493 - 1.21740i) q^{20} +(2.17324 + 1.50898i) q^{21} +(-3.25877 - 0.616760i) q^{22} +8.51382 q^{23} +(-0.809017 + 0.587785i) q^{24} +(0.845349 + 2.60172i) q^{25} +(2.99918 + 0.974493i) q^{26} +(-0.587785 + 0.809017i) q^{27} +(2.49819 - 0.871235i) q^{28} +(0.814675 + 0.264704i) q^{29} +(-1.43114 + 0.465006i) q^{30} +(3.69441 + 5.08492i) q^{31} +1.00000i q^{32} +(-1.59359 + 2.90869i) q^{33} -4.49865i q^{34} +(3.98039 - 0.0851877i) q^{35} +(0.309017 + 0.951057i) q^{36} +(-1.85973 + 5.72367i) q^{37} +(3.73748 - 5.14420i) q^{38} +(1.85360 - 2.55126i) q^{39} +(-0.465006 + 1.43114i) q^{40} +(-3.11905 - 9.59944i) q^{41} +(-0.0566111 - 2.64515i) q^{42} -8.65762i q^{43} +(1.41649 + 2.99893i) q^{44} +1.50479i q^{45} +(-5.00430 - 6.88783i) q^{46} +(1.41837 - 0.460858i) q^{47} +(0.951057 + 0.309017i) q^{48} +(-1.87631 + 6.74385i) q^{49} +(1.60795 - 2.21315i) q^{50} +(-4.27847 - 1.39016i) q^{51} +(-0.974493 - 2.99918i) q^{52} +(0.331296 - 0.240700i) q^{53} +1.00000 q^{54} +(0.632679 + 4.95056i) q^{55} +(-2.17324 - 1.50898i) q^{56} +(-3.73748 - 5.14420i) q^{57} +(-0.264704 - 0.814675i) q^{58} +(5.04243 + 1.63838i) q^{59} +(1.21740 + 0.884493i) q^{60} +(5.80756 + 4.21944i) q^{61} +(1.94227 - 5.97769i) q^{62} +(-2.53318 - 0.763555i) q^{63} +(0.809017 - 0.587785i) q^{64} -4.74539i q^{65} +(3.28987 - 0.420443i) q^{66} -10.5366 q^{67} +(-3.63949 + 2.64424i) q^{68} +(-8.09712 + 2.63092i) q^{69} +(-2.40853 - 3.17013i) q^{70} +(11.6159 + 8.43945i) q^{71} +(0.587785 - 0.809017i) q^{72} +(4.34451 - 13.3710i) q^{73} +(5.72367 - 1.85973i) q^{74} +(-1.60795 - 2.21315i) q^{75} -6.35857 q^{76} +(-8.65485 - 1.44694i) q^{77} -3.15352 q^{78} +(7.69909 + 10.5969i) q^{79} +(1.43114 - 0.465006i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-5.93278 + 8.16577i) q^{82} +(-2.08119 - 1.51207i) q^{83} +(-2.10669 + 1.60058i) q^{84} +(-6.43820 + 2.09190i) q^{85} +(-7.00417 + 5.08882i) q^{86} -0.856600 q^{87} +(1.59359 - 2.90869i) q^{88} +2.90093i q^{89} +(1.21740 - 0.884493i) q^{90} +(7.98844 + 2.40789i) q^{91} +(-2.63092 + 8.09712i) q^{92} +(-5.08492 - 3.69441i) q^{93} +(-1.20654 - 0.876604i) q^{94} +(-9.10001 - 2.95677i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-9.52282 - 13.1070i) q^{97} +(6.55875 - 2.44597i) q^{98} +(0.616760 - 3.25877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9}+O(q^{10}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9	\( 32 q + 8 q^{4} - 10 q^{5} + 8 q^{6} - 10 q^{7} + 8 q^{9} - 4 q^{10} + 8 q^{11} - 2 q^{14} + 6 q^{15} - 8 q^{16} + 12 q^{17} + 16 q^{19} - 10 q^{20} + 8 q^{21} - 4 q^{22} + 8 q^{23} - 8 q^{24} + 6 q^{25} + 20 q^{29} + 50 q^{31} + 16 q^{33} + 32 q^{35} - 8 q^{36} - 16 q^{37} - 6 q^{40} - 40 q^{41} - 10 q^{42} + 12 q^{44} - 28 q^{49} + 40 q^{51} + 32 q^{54} + 40 q^{55} - 8 q^{56} + 10 q^{58} - 60 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} - 10 q^{63} + 8 q^{64} - 8 q^{66} - 16 q^{67} - 12 q^{68} - 30 q^{69} - 18 q^{70} - 48 q^{71} + 74 q^{73} - 40 q^{74} + 24 q^{76} - 70 q^{77} - 60 q^{79} - 8 q^{81} - 20 q^{82} - 4 q^{83} + 2 q^{84} - 10 q^{85} - 36 q^{86} - 20 q^{87} - 16 q^{88} + 4 q^{90} - 60 q^{91} - 8 q^{92} - 10 q^{93} - 20 q^{95} + 8 q^{96} - 60 q^{97} + 40 q^{98} - 8 q^{99}+O(q^{100}) \) 32 * q + 8 * q^4 - 10 * q^5 + 8 * q^6 - 10 * q^7 + 8 * q^9 - 4 * q^10 + 8 * q^11 - 2 * q^14 + 6 * q^15 - 8 * q^16 + 12 * q^17 + 16 * q^19 - 10 * q^20 + 8 * q^21 - 4 * q^22 + 8 * q^23 - 8 * q^24 + 6 * q^25 + 20 * q^29 + 50 * q^31 + 16 * q^33 + 32 * q^35 - 8 * q^36 - 16 * q^37 - 6 * q^40 - 40 * q^41 - 10 * q^42 + 12 * q^44 - 28 * q^49 + 40 * q^51 + 32 * q^54 + 40 * q^55 - 8 * q^56 + 10 * q^58 - 60 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 - 10 * q^63 + 8 * q^64 - 8 * q^66 - 16 * q^67 - 12 * q^68 - 30 * q^69 - 18 * q^70 - 48 * q^71 + 74 * q^73 - 40 * q^74 + 24 * q^76 - 70 * q^77 - 60 * q^79 - 8 * q^81 - 20 * q^82 - 4 * q^83 + 2 * q^84 - 10 * q^85 - 36 * q^86 - 20 * q^87 - 16 * q^88 + 4 * q^90 - 60 * q^91 - 8 * q^92 - 10 * q^93 - 20 * q^95 + 8 * q^96 - 60 * q^97 + 40 * q^98 - 8 * q^99

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