LMFDB - Embedded newform 120.2.w.c.53.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [120,2,Mod(53,120)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(120, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("120.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 120 = 2^{3} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	120.w (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.958204824255$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.8
Character	$\chi$	$=$	120.53
Dual form			120.2.w.c.77.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0941764 - 1.41107i) q^{2} +(-0.416519 - 1.68122i) q^{3} +(-1.98226 + 0.265780i) q^{4} +(1.62104 - 1.54020i) q^{5} +(-2.33310 + 0.746071i) q^{6} +(-0.361989 + 0.361989i) q^{7} +(0.561717 + 2.77209i) q^{8} +(-2.65302 + 1.40052i) q^{9} +O(q^{10})$	\(q+(-0.0941764 - 1.41107i) q^{2} +(-0.416519 - 1.68122i) q^{3} +(-1.98226 + 0.265780i) q^{4} +(1.62104 - 1.54020i) q^{5} +(-2.33310 + 0.746071i) q^{6} +(-0.361989 + 0.361989i) q^{7} +(0.561717 + 2.77209i) q^{8} +(-2.65302 + 1.40052i) q^{9} +(-2.32601 - 2.14236i) q^{10} -2.63380 q^{11} +(1.27249 + 3.22192i) q^{12} +(3.49376 - 3.49376i) q^{13} +(0.544885 + 0.476703i) q^{14} +(-3.26462 - 2.08380i) q^{15} +(3.85872 - 1.05369i) q^{16} +(3.61339 + 3.61339i) q^{17} +(2.22609 + 3.61172i) q^{18} -0.672266 q^{19} +(-2.80397 + 3.48393i) q^{20} +(0.759360 + 0.457809i) q^{21} +(0.248041 + 3.71648i) q^{22} +(4.31851 - 4.31851i) q^{23} +(4.42653 - 2.09900i) q^{24} +(0.255538 - 4.99347i) q^{25} +(-5.25899 - 4.60093i) q^{26} +(3.45963 + 3.87698i) q^{27} +(0.621348 - 0.813767i) q^{28} +4.76080i q^{29} +(-2.63295 + 4.80287i) q^{30} +3.73793 q^{31} +(-1.85024 - 5.34571i) q^{32} +(1.09703 + 4.42800i) q^{33} +(4.75847 - 5.43906i) q^{34} +(-0.0292613 + 1.14434i) q^{35} +(4.88676 - 3.48132i) q^{36} +(-2.82150 - 2.82150i) q^{37} +(0.0633116 + 0.948617i) q^{38} +(-7.32901 - 4.41857i) q^{39} +(5.18015 + 3.62850i) q^{40} +4.10027i q^{41} +(0.574489 - 1.11463i) q^{42} +(-7.57996 + 7.57996i) q^{43} +(5.22087 - 0.700010i) q^{44} +(-2.14356 + 6.35650i) q^{45} +(-6.50044 - 5.68704i) q^{46} +(0.987537 + 0.987537i) q^{47} +(-3.37872 - 6.04849i) q^{48} +6.73793i q^{49} +(-7.07022 + 0.109683i) q^{50} +(4.56987 - 7.57996i) q^{51} +(-5.99698 + 7.85412i) q^{52} +(-0.646149 - 0.646149i) q^{53} +(5.14489 - 5.24691i) q^{54} +(-4.26949 + 4.05659i) q^{55} +(-1.20680 - 0.800131i) q^{56} +(0.280012 + 1.13023i) q^{57} +(6.71784 - 0.448355i) q^{58} -4.92247i q^{59} +(7.02517 + 3.26298i) q^{60} +6.07190i q^{61} +(-0.352025 - 5.27449i) q^{62} +(0.453392 - 1.46734i) q^{63} +(-7.36895 + 3.11426i) q^{64} +(0.282417 - 11.0446i) q^{65} +(6.14492 - 1.96500i) q^{66} +(-0.349085 - 0.349085i) q^{67} +(-8.12305 - 6.20232i) q^{68} +(-9.05912 - 5.46164i) q^{69} +(1.61750 - 0.0664796i) q^{70} +8.63702i q^{71} +(-5.37262 - 6.56772i) q^{72} +(-11.3261 - 11.3261i) q^{73} +(-3.71562 + 4.24706i) q^{74} +(-8.50157 + 1.65026i) q^{75} +(1.33261 - 0.178675i) q^{76} +(0.953406 - 0.953406i) q^{77} +(-5.54472 + 10.7579i) q^{78} +4.07707i q^{79} +(4.63224 - 7.65130i) q^{80} +(5.07707 - 7.43124i) q^{81} +(5.78579 - 0.386149i) q^{82} +(8.53893 + 8.53893i) q^{83} +(-1.62693 - 0.705675i) q^{84} +(11.4228 + 0.292087i) q^{85} +(11.4097 + 9.98203i) q^{86} +(8.00397 - 1.98296i) q^{87} +(-1.47945 - 7.30111i) q^{88} -6.58584 q^{89} +(9.17137 + 2.42609i) q^{90} +2.52941i q^{91} +(-7.41264 + 9.70819i) q^{92} +(-1.55692 - 6.28429i) q^{93} +(1.30049 - 1.48649i) q^{94} +(-1.08977 + 1.03543i) q^{95} +(-8.21668 + 5.33725i) q^{96} +(-0.660859 + 0.660859i) q^{97} +(9.50772 - 0.634554i) q^{98} +(6.98752 - 3.68869i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 4 q^{6}+O(q^{10}) $ 32 * q - 4 * q^6	$ 32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100}) $ 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

$n$	$31$	$41$	$61$	$97$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−0.0941764	−	1.41107i	−0.0665928	−	0.997780i
$2$	−0.0941764	−	1.41107i	−0.0665928	−	0.997780i
$3$	−0.416519	−	1.68122i	−0.240477	−	0.970655i
$3$	−0.416519	−	1.68122i	−0.240477	−	0.970655i
$4$	−1.98226	+	0.265780i	−0.991131	+	0.132890i
$5$	1.62104	−	1.54020i	0.724951	−	0.688801i
$5$	1.62104	−	1.54020i	0.724951	−	0.688801i
$6$	−2.33310	+	0.746071i	−0.952486	+	0.304582i
$7$	−0.361989	+	0.361989i	−0.136819	+	0.136819i	−0.772199	−	0.635380i	$-0.780843\pi$
$7$	−0.361989	+	0.361989i	−0.136819	+	0.136819i	0.635380	+	0.772199i	$0.280843\pi$
$8$	0.561717	+	2.77209i	0.198597	+	0.980081i
$9$	−2.65302	+	1.40052i	−0.884341	+	0.466841i
$10$	−2.32601	−	2.14236i	−0.735548	−	0.677473i
$11$	−2.63380			−0.794119			−0.397060	−	0.917793i	$-0.629969\pi$
$11$	−2.63380			−0.794119			−0.397060	+	0.917793i	$0.629969\pi$
$12$	1.27249	+	3.22192i	0.367335	+	0.930089i
$13$	3.49376	−	3.49376i	0.968995	−	0.968995i	−0.0305386	−	0.999534i	$-0.509722\pi$
$13$	3.49376	−	3.49376i	0.968995	−	0.968995i	0.999534	+	0.0305386i	$0.00972224\pi$
$14$	0.544885	+	0.476703i	0.145627	+	0.127404i
$15$	−3.26462	−	2.08380i	−0.842922	−	0.538036i
$16$	3.85872	−	1.05369i	0.964681	−	0.263423i
$17$	3.61339	+	3.61339i	0.876376	+	0.876376i	0.993158	−	0.116782i	$-0.0372578\pi$
$17$	3.61339	+	3.61339i	0.876376	+	0.876376i	−0.116782	+	0.993158i	$0.537258\pi$
$18$	2.22609	+	3.61172i	0.524696	+	0.851290i
$19$	−0.672266			−0.154228			−0.0771142	−	0.997022i	$-0.524571\pi$
$19$	−0.672266			−0.154228			−0.0771142	+	0.997022i	$0.524571\pi$
$20$	−2.80397	+	3.48393i	−0.626987	+	0.779030i
$21$	0.759360	+	0.457809i	0.165706	+	0.0999022i
$22$	0.248041	+	3.71648i	0.0528826	+	0.792357i
$23$	4.31851	−	4.31851i	0.900472	−	0.900472i	−0.0950052	−	0.995477i	$-0.530287\pi$
$23$	4.31851	−	4.31851i	0.900472	−	0.900472i	0.995477	+	0.0950052i	$0.0302868\pi$
$24$	4.42653	−	2.09900i	0.903562	−	0.428457i
$25$	0.255538	−	4.99347i	0.0511076	−	0.998693i
$26$	−5.25899	−	4.60093i	−1.03137	−	0.902316i
$27$	3.45963	+	3.87698i	0.665806	+	0.746125i
$28$	0.621348	−	0.813767i	0.117424	−	0.153787i
$29$			4.76080i			0.884058i	0.897001	+	0.442029i	$0.145741\pi$
$29$			4.76080i			0.884058i	−0.897001	+	0.442029i	$0.854259\pi$
$30$	−2.63295	+	4.80287i	−0.480709	+	0.876880i
$31$	3.73793			0.671352			0.335676	−	0.941978i	$-0.391035\pi$
$31$	3.73793			0.671352			0.335676	+	0.941978i	$0.391035\pi$
$32$	−1.85024	−	5.34571i	−0.327079	−	0.944997i
$33$	1.09703	+	4.42800i	0.190968	+	0.770816i
$34$	4.75847	−	5.43906i	0.816070	−	0.932791i
$35$	−0.0292613	+	1.14434i	−0.00494606	+	0.193428i
$36$	4.88676	−	3.48132i	0.814459	−	0.580221i
$37$	−2.82150	−	2.82150i	−0.463851	−	0.463851i	0.436064	−	0.899915i	$-0.356372\pi$
$37$	−2.82150	−	2.82150i	−0.463851	−	0.463851i	−0.899915	+	0.436064i	$0.856372\pi$
$38$	0.0633116	+	0.948617i	0.0102705	+	0.153886i
$39$	−7.32901	−	4.41857i	−1.17358	−	0.707538i
$40$	5.18015	+	3.62850i	0.819054	+	0.573717i
$41$			4.10027i			0.640355i	0.947358	+	0.320177i	$0.103743\pi$
$41$			4.10027i			0.640355i	−0.947358	+	0.320177i	$0.896257\pi$
$42$	0.574489	−	1.11463i	0.0886456	−	0.171991i
$43$	−7.57996	+	7.57996i	−1.15593	+	1.15593i	−0.170591	+	0.985342i	$0.554568\pi$
$43$	−7.57996	+	7.57996i	−1.15593	+	1.15593i	−0.985342	+	0.170591i	$0.945432\pi$
$44$	5.22087	−	0.700010i	0.787076	−	0.105530i
$45$	−2.14356	+	6.35650i	−0.319544	+	0.947572i
$46$	−6.50044	−	5.68704i	−0.958438	−	0.838508i
$47$	0.987537	+	0.987537i	0.144047	+	0.144047i	0.775453	−	0.631406i	$-0.217522\pi$
$47$	0.987537	+	0.987537i	0.144047	+	0.144047i	−0.631406	+	0.775453i	$0.717522\pi$
$48$	−3.37872	−	6.04849i	−0.487676	−	0.873025i
$49$			6.73793i			0.962561i
$50$	−7.07022	+	0.109683i	−0.999880	+	0.0155116i
$51$	4.56987	−	7.57996i	0.639910	−	1.06141i
$52$	−5.99698	+	7.85412i	−0.831631	+	1.08917i
$53$	−0.646149	−	0.646149i	−0.0887554	−	0.0887554i	0.661335	−	0.750091i	$-0.269990\pi$
$53$	−0.646149	−	0.646149i	−0.0887554	−	0.0887554i	−0.750091	+	0.661335i	$0.769990\pi$
$54$	5.14489	−	5.24691i	0.700131	−	0.714014i
$55$	−4.26949	+	4.05659i	−0.575698	+	0.546990i
$56$	−1.20680	−	0.800131i	−0.161266	−	0.106922i
$57$	0.280012	+	1.13023i	0.0370884	+	0.149702i
$58$	6.71784	−	0.448355i	0.882096	−	0.0588719i
$59$		−	4.92247i		−	0.640851i	−0.947274	−	0.320425i	$-0.896174\pi$
$59$		−	4.92247i		−	0.640851i	0.947274	−	0.320425i	$-0.103826\pi$
$60$	7.02517	+	3.26298i	0.906945	+	0.421248i
$61$			6.07190i			0.777428i	0.921359	+	0.388714i	$0.127081\pi$
$61$			6.07190i			0.777428i	−0.921359	+	0.388714i	$0.872919\pi$
$62$	−0.352025	−	5.27449i	−0.0447072	−	0.669861i
$63$	0.453392	−	1.46734i	0.0571220	−	0.184868i
$64$	−7.36895	+	3.11426i	−0.921118	+	0.389283i
$65$	0.282417	−	11.0446i	0.0350295	−	1.36992i
$66$	6.14492	−	1.96500i	0.756388	−	0.241875i
$67$	−0.349085	−	0.349085i	−0.0426476	−	0.0426476i	0.685461	−	0.728109i	$-0.259601\pi$
$67$	−0.349085	−	0.349085i	−0.0426476	−	0.0426476i	−0.728109	+	0.685461i	$0.759601\pi$
$68$	−8.12305	−	6.20232i	−0.985064	−	0.752141i
$69$	−9.05912	−	5.46164i	−1.09059	−	0.657504i
$70$	1.61750	−	0.0664796i	0.193328	−	0.00794584i
$71$			8.63702i			1.02503i	0.858680	+	0.512513i	$0.171285\pi$
$71$			8.63702i			1.02503i	−0.858680	+	0.512513i	$0.828715\pi$
$72$	−5.37262	−	6.56772i	−0.633170	−	0.774013i
$73$	−11.3261	−	11.3261i	−1.32562	−	1.32562i	−0.909152	−	0.416465i	$-0.863269\pi$
$73$	−11.3261	−	11.3261i	−1.32562	−	1.32562i	−0.416465	−	0.909152i	$-0.636731\pi$
$74$	−3.71562	+	4.24706i	−0.431932	+	0.493711i
$75$	−8.50157	+	1.65026i	−0.981676	+	0.190555i
$76$	1.33261	−	0.178675i	0.152860	−	0.0204954i
$77$	0.953406	−	0.953406i	0.108651	−	0.108651i
$78$	−5.54472	+	10.7579i	−0.627816	+	1.21809i
$79$			4.07707i			0.458706i	0.973343	+	0.229353i	$0.0736610\pi$
$79$			4.07707i			0.458706i	−0.973343	+	0.229353i	$0.926339\pi$
$80$	4.63224	−	7.65130i	0.517900	−	0.855441i
$81$	5.07707	−	7.43124i	0.564119	−	0.825694i
$82$	5.78579	−	0.386149i	0.638933	−	0.0426430i
$83$	8.53893	+	8.53893i	0.937270	+	0.937270i	0.998145	−	0.0608758i	$-0.0193894\pi$
$83$	8.53893	+	8.53893i	0.937270	+	0.937270i	−0.0608758	+	0.998145i	$0.519389\pi$
$84$	−1.62693	−	0.705675i	−0.177512	−	0.0769955i
$85$	11.4228	+	0.292087i	1.23898	+	0.0316813i
$86$	11.4097	+	9.98203i	1.23034	+	1.07639i
$87$	8.00397	−	1.98296i	0.858115	−	0.212596i
$88$	−1.47945	−	7.30111i	−0.157710	−	0.778301i
$89$	−6.58584			−0.698097			−0.349049	−	0.937105i	$-0.613495\pi$
$89$	−6.58584			−0.698097			−0.349049	+	0.937105i	$0.613495\pi$
$90$	9.17137	+	2.42609i	0.966748	+	0.255733i
$91$			2.52941i			0.265154i
$92$	−7.41264	+	9.70819i	−0.772822	+	1.01215i
$93$	−1.55692	−	6.28429i	−0.161445	−	0.651651i
$94$	1.30049	−	1.48649i	0.134135	−	0.153320i
$95$	−1.08977	+	1.03543i	−0.111808	+	0.106233i
$96$	−8.21668	+	5.33725i	−0.838611	+	0.544731i
$97$	−0.660859	+	0.660859i	−0.0671001	+	0.0671001i	−0.739860	−	0.672760i	$-0.765108\pi$
$97$	−0.660859	+	0.660859i	−0.0671001	+	0.0671001i	0.672760	+	0.739860i	$0.265108\pi$
$98$	9.50772	−	0.634554i	0.960424	−	0.0640996i
$99$	6.98752	−	3.68869i	0.702272	−	0.370728i
$100$	0.820619	+	9.96627i	0.0820619	+	0.996627i
$101$	−3.46850			−0.345129			−0.172564	−	0.984998i	$-0.555205\pi$
$101$	−3.46850			−0.345129			−0.172564	+	0.984998i	$0.555205\pi$
$102$	−11.1263	−	5.73457i	−1.10166	−	0.567807i
$103$	8.68806	+	8.68806i	0.856060	+	0.856060i	0.990871	−	0.134811i	$-0.0430428\pi$
$103$	8.68806	+	8.68806i	0.856060	+	0.856060i	−0.134811	+	0.990871i	$0.543043\pi$
$104$	11.6475	+	7.72251i	1.14213	+	0.757254i
$105$	1.93607	−	0.427443i	0.188941	−	0.0417142i
$106$	−0.850913	+	0.972617i	−0.0826480	+	0.0944689i
$107$	3.10967	−	3.10967i	0.300623	−	0.300623i	−0.540634	−	0.841258i	$-0.681816\pi$
$107$	3.10967	−	3.10967i	0.300623	−	0.300623i	0.841258	+	0.540634i	$0.181816\pi$
$108$	−7.88831	−	6.76569i	−0.759053	−	0.651029i
$109$	4.14320			0.396846			0.198423	−	0.980116i	$-0.436418\pi$
$109$	4.14320			0.396846			0.198423	+	0.980116i	$0.436418\pi$
$110$	6.12623	+	5.64253i	0.584113	+	0.537994i
$111$	−3.56836	+	5.91877i	−0.338693	+	0.561785i
$112$	−1.01539	+	1.77824i	−0.0959455	+	0.168028i
$113$	4.38269	−	4.38269i	0.412289	−	0.412289i	−0.470247	−	0.882535i	$-0.655835\pi$
$113$	4.38269	−	4.38269i	0.412289	−	0.412289i	0.882535	+	0.470247i	$0.155835\pi$
$114$	1.56847	−	0.501558i	0.146900	−	0.0469752i
$115$	0.349085	−	13.6519i	0.0325524	−	1.27304i
$116$	−1.26532	−	9.43715i	−0.117482	−	0.876217i
$117$	−4.37594	+	14.1621i	−0.404555	+	1.30929i
$118$	−6.94597	+	0.463580i	−0.639428	+	0.0426760i
$119$	−2.61602			−0.239810
$120$	3.94270	−	10.2203i	0.359917	−	0.932984i
$121$	−4.06312			−0.369374
$122$	8.56791	−	0.571830i	0.775702	−	0.0517711i
$123$	6.89347	−	1.70784i	0.621563	−	0.153991i
$124$	−7.40955	+	0.993466i	−0.665397	+	0.0892159i
$125$	−7.27672	−	8.48819i	−0.650850	−	0.759206i
$126$	−2.11323	−	0.501580i	−0.188261	−	0.0446843i
$127$	9.88701	−	9.88701i	0.877331	−	0.877331i	−0.115927	−	0.993258i	$-0.536984\pi$
$127$	9.88701	−	9.88701i	0.877331	−	0.877331i	0.993258	+	0.115927i	$0.0369839\pi$
$128$	5.08843	+	10.1048i	0.449758	+	0.893150i
$129$	15.9008	+	9.58641i	1.39999	+	0.844036i
$130$	−15.6114	+	0.641632i	−1.36921	+	0.0562749i
$131$	−8.79462			−0.768389			−0.384195	−	0.923252i	$-0.625521\pi$
$131$	−8.79462			−0.768389			−0.384195	+	0.923252i	$0.625521\pi$
$132$	−3.35147	−	8.48588i	−0.291708	−	0.738601i
$133$	0.243353	−	0.243353i	0.0211014	−	0.0211014i
$134$	−0.459710	+	0.525461i	−0.0397129	+	0.0453929i
$135$	11.5795	+	0.956203i	0.996608	+	0.0822968i
$136$	−7.98693	+	12.0463i	−0.684874	+	1.03297i
$137$	−1.48819	−	1.48819i	−0.127145	−	0.127145i	0.640671	−	0.767816i	$-0.278656\pi$
$137$	−1.48819	−	1.48819i	−0.127145	−	0.127145i	−0.767816	+	0.640671i	$0.778656\pi$
$138$	−6.85362	+	13.2975i	−0.583419	+	1.13195i
$139$	13.3028			1.12833			0.564164	−	0.825663i	$-0.309199\pi$
$139$	13.3028			1.12833			0.564164	+	0.825663i	$0.309199\pi$
$140$	−0.246138	−	2.27615i	−0.0208025	−	0.192370i
$141$	1.24894	−	2.07160i	0.105180	−	0.174460i
$142$	12.1875	−	0.813404i	1.02275	−	0.0682593i
$143$	−9.20185	+	9.20185i	−0.769498	+	0.769498i
$144$	−8.76156	+	8.19970i	−0.730130	+	0.683308i
$145$	7.33261	+	7.71744i	0.608940	+	0.640899i
$146$	−14.9153	+	17.0486i	−1.23440	+	1.41095i
$147$	11.3280	−	2.80648i	0.934314	−	0.231474i
$148$	6.34284	+	4.84305i	0.521378	+	0.398096i
$149$			5.22462i			0.428018i	0.976832	+	0.214009i	$0.0686522\pi$
$149$			5.22462i			0.428018i	−0.976832	+	0.214009i	$0.931348\pi$
$150$	3.12928	+	11.8409i	0.255505	+	0.966808i
$151$	−11.8511			−0.964429			−0.482214	−	0.876053i	$-0.660167\pi$
$151$	−11.8511			−0.964429			−0.482214	+	0.876053i	$0.660167\pi$
$152$	−0.377623	−	1.86358i	−0.0306293	−	0.151156i
$153$	−14.6470	−	4.52577i	−1.18414	−	0.365887i
$154$	−1.43511	−	1.25554i	−0.115645	−	0.101174i
$155$	6.05933	−	5.75717i	0.486697	−	0.462427i
$156$	15.7024	+	6.81087i	1.25720	+	0.545306i
$157$	−13.9522	−	13.9522i	−1.11351	−	1.11351i	−0.992673	−	0.120836i	$-0.961443\pi$
$157$	−13.9522	−	13.9522i	−1.11351	−	1.11351i	−0.120836	−	0.992673i	$-0.538557\pi$
$158$	5.75305	−	0.383964i	0.457688	−	0.0305465i
$159$	−0.817188	+	1.35546i	−0.0648072	+	0.107495i
$160$	−11.2328	−	5.81587i	−0.888030	−	0.459785i
$161$			3.12651i			0.246403i
$162$	−10.9642	−	6.46427i	−0.861427	−	0.507881i
$163$	−6.66434	+	6.66434i	−0.521992	+	0.521992i	−0.918172	−	0.396181i	$-0.870335\pi$
$163$	−6.66434	+	6.66434i	−0.521992	+	0.521992i	0.396181	+	0.918172i	$0.370335\pi$
$164$	−1.08977	−	8.12781i	−0.0850967	−	0.634675i
$165$	8.59835	+	5.48832i	0.669381	+	0.427265i
$166$	11.2449	−	12.8532i	0.872774	−	0.997604i
$167$	−15.6456	−	15.6456i	−1.21069	−	1.21069i	−0.970800	−	0.239890i	$-0.922889\pi$
$167$	−15.6456	−	15.6456i	−1.21069	−	1.21069i	−0.239890	−	0.970800i	$-0.577111\pi$
$168$	−0.842542	+	2.36217i	−0.0650035	+	0.182246i
$169$		−	11.4127i		−	0.877903i
$170$	−0.663602	−	16.1459i	−0.0508960	−	1.23834i
$171$	1.78354	−	0.941524i	0.136390	−	0.0720001i
$172$	13.0109	−	17.0401i	0.992069	−	1.29929i
$173$	−6.40332	−	6.40332i	−0.486836	−	0.486836i	0.420471	−	0.907306i	$-0.361865\pi$
$173$	−6.40332	−	6.40332i	−0.486836	−	0.486836i	−0.907306	+	0.420471i	$0.861865\pi$
$174$	−3.55189	−	11.1074i	−0.269268	−	0.842053i
$175$	1.71508	+	1.90008i	0.129648	+	0.143633i
$176$	−10.1631	+	2.77521i	−0.766071	+	0.209189i
$177$	−8.27577	+	2.05030i	−0.622045	+	0.154110i
$178$	0.620231	+	9.29311i	0.0464882	+	0.696548i
$179$		−	0.582525i		−	0.0435399i	−0.999763	−	0.0217700i	$-0.993070\pi$
$179$		−	0.582525i		−	0.0435399i	0.999763	−	0.0217700i	$-0.00693014\pi$
$180$	2.55967	−	13.1700i	0.190787	−	0.981632i
$181$			3.71429i			0.276081i	0.990427	+	0.138040i	$0.0440804\pi$
$181$			3.71429i			0.276081i	−0.990427	+	0.138040i	$0.955920\pi$
$182$	3.56918	−	0.238211i	0.264565	−	0.0176573i
$183$	10.2082	−	2.52906i	0.754614	−	0.186954i
$184$	14.3971	+	9.54551i	1.06137	+	0.703704i
$185$	−8.91944	−	0.228075i	−0.655770	−	0.0167684i
$186$	−8.72098	+	2.78876i	−0.639453	+	0.204482i
$187$	−9.51693	−	9.51693i	−0.695947	−	0.695947i
$188$	−2.22002	−	1.69509i	−0.161912	−	0.123627i
$189$	−2.65577	−	0.151077i	−0.193179	−	0.0109892i
$190$	1.56369	+	1.44023i	0.113442	+	0.104485i
$191$		−	22.4496i		−	1.62440i	−0.583380	−	0.812199i	$-0.698270\pi$
$191$		−	22.4496i		−	1.62440i	0.583380	−	0.812199i	$-0.301730\pi$
$192$	8.30507	+	11.0917i	0.599367	+	0.800474i
$193$	8.01395	+	8.01395i	0.576857	+	0.576857i	0.934036	−	0.357179i	$-0.116261\pi$
$193$	8.01395	+	8.01395i	0.576857	+	0.576857i	−0.357179	+	0.934036i	$0.616261\pi$
$194$	0.994759	+	0.870284i	0.0714195	+	0.0624828i
$195$	−18.6861	+	4.12549i	−1.33814	+	0.295433i
$196$	−1.79081	−	13.3563i	−0.127915	−	0.954024i
$197$	1.49806	−	1.49806i	0.106733	−	0.106733i	−0.651724	−	0.758456i	$-0.725954\pi$
$197$	1.49806	−	1.49806i	0.106733	−	0.106733i	0.758456	+	0.651724i	$0.225954\pi$
$198$	−5.86308	−	9.51253i	−0.416671	−	0.676026i
$199$		−	12.6160i		−	0.894328i	−0.894452	−	0.447164i	$-0.852434\pi$
$199$		−	12.6160i		−	0.894328i	0.894452	−	0.447164i	$-0.147566\pi$
$200$	13.9859	−	2.09654i	0.988950	−	0.148248i
$201$	−0.441490	+	0.732291i	−0.0311403	+	0.0516519i
$202$	0.326651	+	4.89431i	0.0229831	+	0.344363i
$203$	−1.72336	−	1.72336i	−0.120956	−	0.120956i
$204$	−7.04407	+	16.2400i	−0.493184	+	1.13703i
$205$	6.31526	+	6.64670i	0.441077	+	0.464226i
$206$	11.4413	−	13.0777i	0.797152	−	0.911167i
$207$	−5.40893	+	17.5053i	−0.375947	+	1.21670i
$208$	9.80011	−	17.1628i	0.679515	−	1.19003i
$209$	1.77061			0.122476
$210$	−0.785487	−	2.69169i	−0.0542037	−	0.185744i
$211$			14.0010i			0.963865i	0.876208	+	0.481933i	$0.160065\pi$
$211$			14.0010i			0.963865i	−0.876208	+	0.481933i	$0.839935\pi$
$212$	1.45257	+	1.10910i	0.0997630	+	0.0761736i
$213$	14.5208	−	3.59748i	0.994946	−	0.246496i
$214$	−4.68083	−	4.09512i	−0.319975	−	0.279937i
$215$	−0.612724	+	23.9621i	−0.0417874	+	1.63420i
$216$	−8.80400	+	11.7682i	−0.599036	+	0.800722i
$217$	−1.35309	+	1.35309i	−0.0918537	+	0.0918537i
$218$	−0.390192	−	5.84636i	−0.0264271	−	0.395965i
$219$	−14.3241	+	23.7592i	−0.967935	+	1.60550i
$220$	7.38508	−	9.17596i	0.497902	−	0.618643i
$221$	25.2486			1.69841
$222$	8.68788	+	4.47781i	0.583092	+	0.300531i
$223$	−2.56530	−	2.56530i	−0.171785	−	0.171785i	0.615978	−	0.787763i	$-0.288761\pi$
$223$	−2.56530	−	2.56530i	−0.171785	−	0.171785i	−0.787763	+	0.615978i	$0.788761\pi$
$224$	2.60486	+	1.26532i	0.174044	+	0.0845431i
$225$	6.31552	+	13.6057i	0.421034	+	0.907045i
$226$	−6.59704	−	5.77155i	−0.438829	−	0.383918i
$227$	−13.3645	+	13.3645i	−0.887032	+	0.887032i	−0.994237	−	0.107205i	$-0.965810\pi$
$227$	−13.3645	+	13.3645i	−0.887032	+	0.887032i	0.107205	+	0.994237i	$0.465810\pi$
$228$	−0.855448	−	2.16599i	−0.0566534	−	0.143446i
$229$	−15.7606			−1.04149			−0.520746	−	0.853712i	$-0.674346\pi$
$229$	−15.7606			−1.04149			−0.520746	+	0.853712i	$0.674346\pi$
$230$	−19.2967	+	0.793098i	−1.27238	+	0.0522953i
$231$	−2.00000	−	1.20578i	−0.131590	−	0.0793343i
$232$	−13.1974	+	2.67422i	−0.866449	+	0.175571i
$233$	−13.0197	+	13.0197i	−0.852949	+	0.852949i	−0.990495	−	0.137546i	$-0.956079\pi$
$233$	−13.0197	+	13.0197i	−0.852949	+	0.852949i	0.137546	+	0.990495i	$0.456079\pi$
$234$	20.3959	+	4.84103i	1.33332	+	0.316468i
$235$	3.12185	+	0.0798273i	0.203647	+	0.00520736i
$236$	1.30829	+	9.75762i	0.0851626	+	0.635167i
$237$	6.85446	−	1.69818i	0.445245	−	0.110308i
$238$	0.246367	+	3.69139i	0.0159696	+	0.239278i
$239$	24.8336			1.60635			0.803177	−	0.595740i	$-0.203141\pi$
$239$	24.8336			1.60635			0.803177	+	0.595740i	$0.203141\pi$
$240$	−14.7930	−	4.60092i	−0.954881	−	0.296988i
$241$	17.2991			1.11433			0.557165	−	0.830402i	$-0.311889\pi$
$241$	17.2991			1.11433			0.557165	+	0.830402i	$0.311889\pi$
$242$	0.382650	+	5.73336i	0.0245977	+	0.368555i
$243$	−14.6083	−	5.44043i	−0.937121	−	0.349004i
$244$	−1.61379	−	12.0361i	−0.103312	−	0.770532i
$245$	10.3778	+	10.9224i	0.663013	+	0.697810i
$246$	−3.05909	−	9.56636i	−0.195041	−	0.609929i
$247$	−2.34874	+	2.34874i	−0.149446	+	0.149446i
$248$	2.09966	+	10.3619i	0.133328	+	0.657979i
$249$	10.7992	−	17.9125i	0.684373	−	1.13516i
$250$	−11.2922	+	11.0674i	−0.714179	+	0.699963i
$251$	−1.05032			−0.0662958			−0.0331479	−	0.999450i	$-0.510553\pi$
$251$	−1.05032			−0.0662958			−0.0331479	+	0.999450i	$0.510553\pi$
$252$	−0.508751	+	3.02916i	−0.0320483	+	0.190819i
$253$	−11.3741	+	11.3741i	−0.715082	+	0.715082i
$254$	−14.8824	−	13.0202i	−0.933807	−	0.816959i
$255$	−4.26675	−	19.3260i	−0.267195	−	1.21024i
$256$	13.7795	−	8.13180i	0.861217	−	0.508237i
$257$	2.20315	+	2.20315i	0.137429	+	0.137429i	0.772474	−	0.635046i	$-0.219019\pi$
$257$	2.20315	+	2.20315i	0.137429	+	0.137429i	−0.635046	+	0.772474i	$0.719019\pi$
$258$	12.0297	−	23.3400i	0.748934	−	1.45309i
$259$	2.04270			0.126927
$260$	2.37562	+	21.9684i	0.147329	+	1.36242i
$261$	−6.66761	−	12.6305i	−0.412715	−	0.781809i
$262$	0.828245	+	12.4099i	0.0511692	+	0.766683i
$263$	7.49936	−	7.49936i	0.462430	−	0.462430i	−0.437021	−	0.899451i	$-0.643966\pi$
$263$	7.49936	−	7.49936i	0.462430	−	0.462430i	0.899451	+	0.437021i	$0.143966\pi$
$264$	−11.6586	+	5.52834i	−0.717536	+	0.340246i
$265$	−2.04264	−	0.0522313i	−0.125478	−	0.00320854i
$266$	−0.366307	−	0.320471i	−0.0224597	−	0.0196493i
$267$	2.74313	+	11.0723i	0.167877	+	0.677611i
$268$	0.784759	+	0.599199i	0.0479368	+	0.0366019i
$269$			21.1993i			1.29254i	0.763108	+	0.646271i	$0.223673\pi$
$269$			21.1993i			1.29254i	−0.763108	+	0.646271i	$0.776327\pi$
$270$	0.258754	−	16.4296i	0.0157473	−	0.999876i
$271$	−14.6748			−0.891431			−0.445716	−	0.895175i	$-0.647051\pi$
$271$	−14.6748			−0.891431			−0.445716	+	0.895175i	$0.647051\pi$
$272$	17.7505	+	10.1357i	1.07628	+	0.614565i
$273$	4.25250	−	1.05355i	0.257373	−	0.0637636i
$274$	−1.95980	+	2.24010i	−0.118396	+	0.135330i
$275$	−0.673036	+	13.1518i	−0.0405856	+	0.793082i
$276$	19.4091	+	8.41866i	1.16829	+	0.506744i
$277$	8.79593	+	8.79593i	0.528496	+	0.528496i	0.920124	−	0.391628i	$-0.128088\pi$
$277$	8.79593	+	8.79593i	0.528496	+	0.528496i	−0.391628	+	0.920124i	$0.628088\pi$
$278$	−1.25281	−	18.7712i	−0.0751384	−	1.12582i
$279$	−9.91681	+	5.23506i	−0.593704	+	0.313415i
$280$	−3.18864	+	0.561679i	−0.190558	+	0.0335667i
$281$		−	0.490821i		−	0.0292799i	−0.999893	−	0.0146399i	$-0.995340\pi$
$281$		−	0.490821i		−	0.0292799i	0.999893	−	0.0146399i	$-0.00466021\pi$
$282$	−3.04080	−	1.56726i	−0.181077	−	0.0933287i
$283$	9.43710	−	9.43710i	0.560978	−	0.560978i	−0.368608	−	0.929585i	$-0.620165\pi$
$283$	9.43710	−	9.43710i	0.560978	−	0.560978i	0.929585	+	0.368608i	$0.120165\pi$
$284$	−2.29555	−	17.1208i	−0.136216	−	1.01593i
$285$	2.19469	+	1.40087i	0.130002	+	0.0829804i
$286$	13.8511	+	12.1179i	0.819033	+	0.716547i
$287$	−1.48425	−	1.48425i	−0.0876127	−	0.0876127i
$288$	12.3955	+	11.5910i	0.730413	+	0.683006i
$289$			9.11317i			0.536069i
$290$	10.1993	−	11.0737i	0.598925	−	0.650267i
$291$	1.38631	+	0.835791i	0.0812671	+	0.0489950i
$292$	25.4615	+	19.4410i	1.49002	+	1.13770i
$293$	−4.01316	−	4.01316i	−0.234451	−	0.234451i	0.580096	−	0.814548i	$-0.303015\pi$
$293$	−4.01316	−	4.01316i	−0.234451	−	0.234451i	−0.814548	+	0.580096i	$0.803015\pi$
$294$	−5.02697	−	15.7203i	−0.293179	−	0.916826i
$295$	−7.58161	−	7.97952i	−0.441418	−	0.464585i
$296$	6.23655	−	9.40632i	0.362492	−	0.546731i
$297$	−9.11195	−	10.2112i	−0.528729	−	0.592512i
$298$	7.37233	−	0.492036i	0.427068	−	0.0285029i
$299$		−	30.1757i		−	1.74510i
$300$	16.4137	−	5.53079i	0.947647	−	0.319320i
$301$		−	5.48773i		−	0.316307i
$302$	1.11609	+	16.7228i	0.0642240	+	0.962288i
$303$	1.44470	+	5.83132i	0.0829957	+	0.335001i
$304$	−2.59409	+	0.708360i	−0.148781	+	0.0406272i
$305$	9.35198	+	9.84280i	0.535493	+	0.563597i
$306$	−5.00679	+	21.0943i	−0.286219	+	1.20588i
$307$	8.00887	+	8.00887i	0.457091	+	0.457091i	0.897699	−	0.440609i	$-0.145237\pi$
$307$	8.00887	+	8.00887i	0.457091	+	0.457091i	−0.440609	+	0.897699i	$0.645237\pi$
$308$	−1.63650	+	2.14330i	−0.0932485	+	0.122126i
$309$	10.9878	−	18.2253i	0.625076	−	1.03680i
$310$	−8.69445	−	8.00797i	−0.493811	−	0.454822i
$311$		−	12.8874i		−	0.730778i	−0.930855	−	0.365389i	$-0.880936\pi$
$311$		−	12.8874i		−	0.730778i	0.930855	−	0.365389i	$-0.119064\pi$
$312$	8.13185	−	22.7987i	0.460375	−	1.29072i
$313$	12.2991	+	12.2991i	0.695184	+	0.695184i	0.963368	−	0.268184i	$-0.0864235\pi$
$313$	12.2991	+	12.2991i	0.695184	+	0.695184i	−0.268184	+	0.963368i	$0.586424\pi$
$314$	−18.3736	+	21.0016i	−1.03688	+	1.18519i
$315$	−1.52504	−	3.07693i	−0.0859262	−	0.173366i
$316$	−1.08360	−	8.08182i	−0.0609574	−	0.454638i
$317$	9.24176	−	9.24176i	0.519069	−	0.519069i	−0.398221	−	0.917290i	$-0.630372\pi$
$317$	9.24176	−	9.24176i	0.519069	−	0.519069i	0.917290	+	0.398221i	$0.130372\pi$
$318$	1.98961	+	1.02546i	0.111572	+	0.0575050i
$319$		−	12.5390i		−	0.702048i
$320$	−7.14876	+	16.3980i	−0.399628	+	0.916678i
$321$	−6.52329	−	3.93281i	−0.364094	−	0.219508i
$322$	4.41174	−	0.294443i	0.245856	−	0.0164087i
$323$	−2.42916	−	2.42916i	−0.135162	−	0.135162i
$324$	−8.08900	+	16.0801i	−0.449389	+	0.893336i
$325$	−16.5532	−	18.3388i	−0.918206	−	1.01725i
$326$	10.0315	+	8.77626i	0.555594	+	0.486072i
$327$	−1.72572	−	6.96564i	−0.0954326	−	0.385201i
$328$	−11.3663	+	2.30319i	−0.627600	+	0.127173i
$329$	−0.714956			−0.0394168
$330$	6.93466	−	12.6498i	0.381740	−	0.696347i
$331$		−	22.2355i		−	1.22218i	−0.791563	−	0.611088i	$-0.790732\pi$
$331$		−	22.2355i		−	1.22218i	0.791563	−	0.611088i	$-0.209268\pi$
$332$	−19.1959	−	14.6569i	−1.05351	−	0.804403i
$333$	11.4371	+	3.53392i	0.626747	+	0.193658i
$334$	−20.6036	+	23.5505i	−1.12738	+	1.28863i
$335$	−1.10354	−	0.0282182i	−0.0602931	−	0.00154173i
$336$	3.41255	+	0.966428i	0.186170	+	0.0527230i
$337$	−8.98693	+	8.98693i	−0.489549	+	0.489549i	−0.908164	−	0.418615i	$-0.862516\pi$
$337$	−8.98693	+	8.98693i	−0.489549	+	0.489549i	0.418615	+	0.908164i	$0.362516\pi$
$338$	−16.1042	+	1.07481i	−0.875954	+	0.0584620i
$339$	−9.19375	−	5.54280i	−0.499336	−	0.301044i
$340$	−22.7206	+	2.45696i	−1.23220	+	0.133247i
$341$	−9.84494			−0.533133
$342$	−1.49653	−	2.42803i	−0.0809229	−	0.131293i
$343$	−4.97298	−	4.97298i	−0.268516	−	0.268516i
$344$	−25.2701	−	16.7545i	−1.36247	−	0.903343i
$345$	−23.0972	+	5.09937i	−1.24351	+	0.274541i
$346$	−8.43252	+	9.63861i	−0.453335	+	0.518175i
$347$	9.25494	−	9.25494i	0.496831	−	0.496831i	−0.413619	−	0.910450i	$-0.635735\pi$
$347$	9.25494	−	9.25494i	0.496831	−	0.496831i	0.910450	+	0.413619i	$0.135735\pi$
$348$	−15.3389	+	6.05805i	−0.822253	+	0.324745i
$349$	17.5919			0.941671			0.470835	−	0.882221i	$-0.343953\pi$
$349$	17.5919			0.941671			0.470835	+	0.882221i	$0.343953\pi$
$350$	2.51964	−	2.59905i	0.134680	−	0.138925i
$351$	25.6324	+	1.45813i	1.36815	+	0.0778292i
$352$	4.87314	+	14.0795i	0.259739	+	0.750440i
$353$	12.9654	−	12.9654i	0.690077	−	0.690077i	−0.272172	−	0.962249i	$-0.587742\pi$
$353$	12.9654	−	12.9654i	0.690077	−	0.690077i	0.962249	+	0.272172i	$0.0877419\pi$
$354$	3.67251	+	11.4846i	0.195192	+	0.610402i
$355$	13.3028	+	14.0010i	0.706038	+	0.743093i
$356$	13.0549	−	1.75038i	0.691906	−	0.0927701i
$357$	1.08962	+	4.39811i	0.0576689	+	0.232773i
$358$	−0.821985	+	0.0548601i	−0.0434433	+	0.00289945i
$359$	16.5244			0.872125			0.436063	−	0.899916i	$-0.356373\pi$
$359$	16.5244			0.872125			0.436063	+	0.899916i	$0.356373\pi$
$360$	−18.8249	−	2.37159i	−0.992158	−	0.124994i
$361$	−18.5481			−0.976214
$362$	5.24113	−	0.349798i	0.275468	−	0.0183850i
$363$	1.69237	+	6.83101i	0.0888262	+	0.358535i
$364$	−0.672266	−	5.01395i	−0.0352363	−	0.262802i
$365$	−35.8045	−	0.915540i	−1.87409	−	0.0479215i
$366$	−4.53007	−	14.1664i	−0.236791	−	0.740489i
$367$	−24.4900	+	24.4900i	−1.27837	+	1.27837i	−0.336786	+	0.941581i	$0.609340\pi$
$367$	−24.4900	+	24.4900i	−1.27837	+	1.27837i	−0.941581	+	0.336786i	$0.890660\pi$
$368$	12.1136	−	21.2143i	0.631463	−	1.10587i
$369$	−5.74253	−	10.8781i	−0.298944	−	0.566292i
$370$	0.518170	+	12.6075i	0.0269384	+	0.655431i
$371$	0.467798			0.0242869
$372$	4.75646	+	12.0433i	0.246611	+	0.624417i
$373$	0.406084	−	0.406084i	0.0210262	−	0.0210262i	−0.696516	−	0.717542i	$-0.745267\pi$
$373$	0.406084	−	0.406084i	0.0210262	−	0.0210262i	0.717542	+	0.696516i	$0.245267\pi$
$374$	−12.5328	+	14.3254i	−0.648057	+	0.740747i
$375$	−11.2396	+	15.7693i	−0.580413	+	0.814323i
$376$	−2.18282	+	3.29226i	−0.112571	+	0.169785i
$377$	16.6331	+	16.6331i	0.856648	+	0.856648i
$378$	0.0369302	+	3.76172i	0.00189948	+	0.193482i
$379$	5.73108			0.294386			0.147193	−	0.989108i	$-0.452976\pi$
$379$	5.73108			0.294386			0.147193	+	0.989108i	$0.452976\pi$
$380$	1.88501	−	2.34213i	0.0966991	−	0.120149i
$381$	−20.7404	−	12.5041i	−1.06256	−	0.640607i
$382$	−31.6781	+	2.11423i	−1.62079	+	0.108173i
$383$	−17.2603	+	17.2603i	−0.881958	+	0.881958i	−0.993734	−	0.111775i	$-0.964346\pi$
$383$	−17.2603	+	17.2603i	−0.881958	+	0.881958i	0.111775	+	0.993734i	$0.464346\pi$
$384$	14.8691	−	12.7637i	0.758784	−	0.651342i
$385$	0.0770683	−	3.01395i	0.00392776	−	0.153605i
$386$	10.5536	−	12.0630i	0.537162	−	0.613991i
$387$	9.49390	−	30.7257i	0.482602	−	1.56188i
$388$	1.13435	−	1.48564i	0.0575880	−	0.0754219i
$389$		−	27.9300i		−	1.41611i	−0.706159	−	0.708053i	$-0.749574\pi$
$389$		−	27.9300i		−	1.41611i	0.706159	−	0.708053i	$-0.250426\pi$
$390$	7.58117	+	25.9790i	0.383888	+	1.31550i
$391$	31.2089			1.57830
$392$	−18.6781	+	3.78481i	−0.943388	+	0.191162i
$393$	3.66313	+	14.7857i	0.184780	+	0.745841i
$394$	−2.25496	−	1.97280i	−0.113603	−	0.0993881i
$395$	6.27952	+	6.60909i	0.315957	+	0.332539i
$396$	−12.8707	+	9.16910i	−0.646778	+	0.460764i
$397$	3.16232	+	3.16232i	0.158712	+	0.158712i	0.781996	−	0.623284i	$-0.214202\pi$
$397$	3.16232	+	3.16232i	0.158712	+	0.158712i	−0.623284	+	0.781996i	$0.714202\pi$
$398$	−17.8022	+	1.18813i	−0.892342	+	0.0595558i
$399$	−0.510492	−	0.307770i	−0.0255566	−	0.0154077i
$400$	−4.27552	−	19.5377i	−0.213776	−	0.976883i
$401$		−	11.2530i		−	0.561950i	−0.959715	−	0.280975i	$-0.909342\pi$
$401$		−	11.2530i		−	0.561950i	0.959715	−	0.280975i	$-0.0906578\pi$
$402$	1.07490	+	0.554010i	0.0536109	+	0.0276315i
$403$	13.0594	−	13.0594i	0.650536	−	0.650536i
$404$	6.87548	−	0.921858i	0.342068	−	0.0458641i
$405$	−3.21551	−	19.8661i	−0.159780	−	0.987153i
$406$	−2.26949	+	2.59409i	−0.112633	+	0.128742i
$407$	7.43124	+	7.43124i	0.368353	+	0.368353i
$408$	23.5793	+	8.41028i	1.16735	+	0.416371i
$409$			5.05965i			0.250183i	0.992145	+	0.125092i	$0.0399225\pi$
$409$			5.05965i			0.250183i	−0.992145	+	0.125092i	$0.960077\pi$
$410$	8.78424	−	9.53726i	0.433823	−	0.471012i
$411$	−1.88212	+	3.12185i	−0.0928384	+	0.153989i
$412$	−19.5311	−	14.9129i	−0.962229	−	0.734706i
$413$	1.78188	+	1.78188i	0.0876806	+	0.0876806i
$414$	25.2106	+	5.98382i	1.23904	+	0.294089i
$415$	26.9937	+	0.690242i	1.32507	+	0.0338826i
$416$	−25.1409	−	12.2124i	−1.23264	−	0.598760i
$417$	−5.54086	−	22.3649i	−0.271337	−	1.09522i
$418$	−0.166750	−	2.49846i	−0.00815600	−	0.122204i
$419$			25.1822i			1.23023i	0.788436	+	0.615116i	$0.210891\pi$
$419$			25.1822i			1.23023i	−0.788436	+	0.615116i	$0.789109\pi$
$420$	−3.72420	+	1.36187i	−0.181722	+	0.0664526i
$421$			31.5091i			1.53566i	0.640654	+	0.767830i	$0.278664\pi$
$421$			31.5091i			1.53566i	−0.640654	+	0.767830i	$0.721336\pi$
$422$	19.7564	−	1.31856i	0.961726	−	0.0641865i
$423$	−4.00303	−	1.23689i	−0.194634	−	0.0601397i
$424$	1.42823	−	2.15414i	0.0693610	−	0.104614i
$425$	18.9667	−	17.1200i	0.920020	−	0.830441i
$426$	−6.44383	−	20.1511i	−0.312205	−	0.976323i
$427$	−2.19796	−	2.19796i	−0.106367	−	0.106367i
$428$	−5.33769	+	6.99067i	−0.258007	+	0.337907i
$429$	19.3031	+	11.6376i	0.931963	+	0.561870i
$430$	33.8700	−	1.39207i	1.63336	−	0.0671314i
$431$			13.6082i			0.655482i	0.944768	+	0.327741i	$0.106287\pi$
$431$			13.6082i			0.655482i	−0.944768	+	0.327741i	$0.893713\pi$
$432$	17.4349	+	11.3148i	0.838836	+	0.544384i
$433$	2.81500	+	2.81500i	0.135280	+	0.135280i	0.771504	−	0.636224i	$-0.219505\pi$
$433$	2.81500	+	2.81500i	0.135280	+	0.135280i	−0.636224	+	0.771504i	$0.719505\pi$
$434$	2.03674	+	1.78188i	0.0977666	+	0.0855330i
$435$	9.92058	−	15.5422i	0.475655	−	0.745192i
$436$	−8.21290	+	1.10118i	−0.393327	+	0.0527369i
$437$	−2.90319	+	2.90319i	−0.138878	+	0.138878i
$438$	34.8750	+	17.9749i	1.66639	+	0.858872i
$439$			5.56599i			0.265650i	0.991139	+	0.132825i	$0.0424049\pi$
$439$			5.56599i			0.265650i	−0.991139	+	0.132825i	$0.957595\pi$
$440$	−13.6435	−	9.55674i	−0.650426	−	0.455600i
$441$	−9.43663	−	17.8759i	−0.449363	−	0.851232i
$442$	−2.37783	−	35.6277i	−0.113102	−	1.69464i
$443$	−3.53450	−	3.53450i	−0.167929	−	0.167929i	0.618139	−	0.786069i	$-0.287887\pi$
$443$	−3.53450	−	3.53450i	−0.167929	−	0.167929i	−0.786069	+	0.618139i	$0.787887\pi$
$444$	5.50033	−	12.6809i	0.261034	−	0.601811i
$445$	−10.6759	+	10.1435i	−0.506086	+	0.480850i
$446$	−3.37823	+	3.86141i	−0.159964	+	0.182843i
$447$	8.78376	−	2.17616i	0.415458	−	0.102929i
$448$	1.54015	−	3.79481i	0.0727653	−	0.179288i
$449$	−21.1895			−0.999995			−0.499998	−	0.866027i	$-0.666666\pi$
$449$	−21.1895			−0.999995			−0.499998	+	0.866027i	$0.666666\pi$
$450$	18.6038	−	10.1930i	0.876993	−	0.480502i
$451$		−	10.7993i		−	0.508518i
$452$	−7.52280	+	9.85246i	−0.353843	+	0.463421i
$453$	4.93621	+	19.9243i	0.231923	+	0.936127i
$454$	20.1169	+	17.5997i	0.944133	+	0.825993i
$455$	3.89581	+	4.10027i	0.182638	+	0.192224i
$456$	−2.97581	+	1.41109i	−0.139355	+	0.0660802i
$457$	16.8790	−	16.8790i	0.789566	−	0.789566i	−0.191857	−	0.981423i	$-0.561451\pi$
$457$	16.8790	−	16.8790i	0.789566	−	0.789566i	0.981423	+	0.191857i	$0.0614509\pi$
$458$	1.48428	+	22.2394i	0.0693558	+	1.03918i
$459$	−1.50806	+	26.5100i	−0.0703901	+	1.23738i
$460$	2.93641	+	27.1543i	0.136911	+	1.26608i
$461$	3.58886			0.167150			0.0835749	−	0.996502i	$-0.473366\pi$
$461$	3.58886			0.167150			0.0835749	+	0.996502i	$0.473366\pi$
$462$	−1.51309	+	2.93570i	−0.0703952	+	0.136581i
$463$	−26.4996	−	26.4996i	−1.23154	−	1.23154i	−0.963372	−	0.268168i	$-0.913582\pi$
$463$	−26.4996	−	26.4996i	−1.23154	−	1.23154i	−0.268168	−	0.963372i	$-0.586418\pi$
$464$	5.01641	+	18.3706i	0.232881	+	0.852834i
$465$	−12.2029	−	7.78911i	−0.565897	−	0.361211i
$466$	19.5979	+	17.1456i	0.907856	+	0.794256i
$467$	−21.1839	+	21.1839i	−0.980274	+	0.980274i	−0.999809	−	0.0195348i	$-0.993781\pi$
$467$	−21.1839	+	21.1839i	−0.980274	+	0.980274i	0.0195348	+	0.999809i	$0.493781\pi$
$468$	4.91024	−	29.2361i	0.226976	−	1.35144i
$469$	0.252730			0.0116700
$470$	−0.181362	−	4.41268i	−0.00836561	−	0.203542i
$471$	−17.6454	+	29.2682i	−0.813058	+	1.34861i
$472$	13.6455	−	2.76504i	0.628086	−	0.127271i
$473$	19.9641	−	19.9641i	0.917949	−	0.917949i
$474$	−3.04178	−	9.51223i	−0.139714	−	0.436911i
$475$	−0.171790	+	3.35694i	−0.00788225	+	0.154027i
$476$	5.18563	−	0.695284i	0.237683	−	0.0318683i
$477$	2.61920	+	0.809302i	0.119925	+	0.0370554i
$478$	−2.33874	−	35.0421i	−0.106972	−	1.60279i
$479$	−2.58847			−0.118270			−0.0591350	−	0.998250i	$-0.518834\pi$
$479$	−2.58847			−0.118270			−0.0591350	+	0.998250i	$0.518834\pi$
$480$	−5.09910	+	21.3073i	−0.232741	+	0.972539i
$481$	−19.7153			−0.898939
$482$	−1.62916	−	24.4103i	−0.0742063	−	1.11186i
$483$	5.25636	−	1.30225i	0.239173	−	0.0592545i
$484$	8.05417	−	1.07990i	0.366098	−	0.0490861i
$485$	−0.0534204	+	2.08914i	−0.00242569	+	0.0948628i
$486$	−6.30110	+	21.1257i	−0.285824	+	0.958282i
$487$	8.29975	−	8.29975i	0.376098	−	0.376098i	−0.493595	−	0.869692i	$-0.664317\pi$
$487$	8.29975	−	8.29975i	0.376098	−	0.376098i	0.869692	+	0.493595i	$0.164317\pi$
$488$	−16.8319	+	3.41069i	−0.761942	+	0.154395i
$489$	13.9801	+	8.42842i	0.632201	+	0.381146i
$490$	14.4350	−	15.6725i	0.652109	−	0.708010i
$491$	25.3703			1.14494			0.572472	−	0.819924i	$-0.305985\pi$
$491$	25.3703			1.14494			0.572472	+	0.819924i	$0.305985\pi$
$492$	−13.2108	+	5.21753i	−0.595587	+	0.235225i
$493$	−17.2026	+	17.2026i	−0.774767	+	0.774767i
$494$	3.53544	+	3.09305i	0.159067	+	0.139163i
$495$	5.64571	−	16.7417i	0.253756	−	0.752485i
$496$	14.4236	−	3.93862i	0.647640	−	0.176849i
$497$	−3.12651	−	3.12651i	−0.140243	−	0.140243i
$498$	−26.2929	−	13.5516i	−1.17821	−	0.607261i
$499$	−28.6742			−1.28363			−0.641816	−	0.766859i	$-0.721819\pi$
$499$	−28.6742			−1.28363			−0.641816	+	0.766859i	$0.721819\pi$
$500$	16.6804	+	14.8918i	0.745968	+	0.665982i
$501$	−19.7870	+	32.8204i	−0.884018	+	1.46631i
$502$	0.0989156	+	1.48208i	0.00441482	+	0.0661486i
$503$	−5.46994	+	5.46994i	−0.243893	+	0.243893i	−0.818458	−	0.574566i	$-0.805171\pi$
$503$	−5.46994	+	5.46994i	−0.243893	+	0.243893i	0.574566	+	0.818458i	$0.305171\pi$
$504$	4.32228	+	0.432611i	0.192529	+	0.0192700i
$505$	−5.62258	+	5.34220i	−0.250201	+	0.237725i
$506$	17.1208	+	14.9785i	0.761114	+	0.665875i
$507$	−19.1874	+	4.75362i	−0.852140	+	0.211116i
$508$	−16.9709	+	22.2264i	−0.752961	+	0.986138i
$509$			21.6722i			0.960605i	0.877103	+	0.480303i	$0.159473\pi$
$509$			21.6722i			0.960605i	−0.877103	+	0.480303i	$0.840527\pi$
$510$	−26.8685	+	7.84076i	−1.18976	+	0.347195i
$511$	8.19983			0.362739
$512$	−12.7723	−	18.6780i	−0.564460	−	0.825460i
$513$	−2.32579	−	2.60636i	−0.102686	−	0.115074i
$514$	2.90132	−	3.31629i	0.127972	−	0.146275i
$515$	27.4651	+	0.702297i	1.21026	+	0.0309469i
$516$	−34.0674	−	14.7767i	−1.49974	−	0.650506i
$517$	−2.60097	−	2.60097i	−0.114391	−	0.114391i
$518$	−0.192374	−	2.88240i	−0.00845244	−	0.126646i
$519$	−8.09831	+	13.4325i	−0.355476	+	0.589622i
$520$	30.7753	−	5.42108i	1.34959	−	0.237730i
$521$			13.0236i			0.570576i	0.958442	+	0.285288i	$0.0920893\pi$
$521$			13.0236i			0.570576i	−0.958442	+	0.285288i	$0.907911\pi$
$522$	−17.1947	+	10.5980i	−0.752590	+	0.463861i
$523$	1.57962	−	1.57962i	0.0690720	−	0.0690720i	−0.671727	−	0.740799i	$-0.734447\pi$
$523$	1.57962	−	1.57962i	0.0690720	−	0.0690720i	0.740799	+	0.671727i	$0.234447\pi$
$524$	17.4332	−	2.33743i	0.761574	−	0.102111i
$525$	2.48010	−	3.67485i	0.108240	−	0.160384i
$526$	−11.2884	−	9.87589i	−0.492198	−	0.430609i
$527$	13.5066	+	13.5066i	0.588356	+	0.588356i
$528$	8.89886	+	15.9305i	0.387273	+	0.693286i
$529$		−	14.2991i		−	0.621698i
$530$	0.118666	+	2.88723i	0.00515452	+	0.125413i
$531$	6.89403	+	13.0594i	0.299176	+	0.566731i
$532$	−0.417711	+	0.547068i	−0.0181101	+	0.0237184i
$533$	14.3254	+	14.3254i	0.620501	+	0.620501i
$534$	15.3654	−	4.91350i	0.664928	−	0.212628i
$535$	0.251369	−	9.83043i	0.0108676	−	0.425007i
$536$	0.771608	−	1.16378i	0.0333284	−	0.0502678i
$537$	−0.979354	+	0.242633i	−0.0422622	+	0.0104704i
$538$	29.9137	−	1.99647i	1.28967	−	0.0860740i
$539$		−	17.7463i		−	0.764388i
$540$	−23.2078	+	1.18216i	−0.998705	+	0.0508722i
$541$		−	38.6062i		−	1.65981i	−0.557903	−	0.829906i	$-0.688394\pi$
$541$		−	38.6062i		−	1.65981i	0.557903	−	0.829906i	$-0.311606\pi$
$542$	1.38202	+	20.7072i	0.0593629	+	0.889452i
$543$	6.24454	−	1.54707i	0.267979	−	0.0663912i
$544$	12.6305	−	26.0018i	0.541529	−	1.11482i
$545$	6.71629	−	6.38137i	0.287694	−	0.273348i
$546$	−1.88712	−	5.90137i	−0.0807612	−	0.252556i
$547$	−16.8276	−	16.8276i	−0.719498	−	0.719498i	0.249005	−	0.968502i	$-0.419897\pi$
$547$	−16.8276	−	16.8276i	−0.719498	−	0.719498i	−0.968502	+	0.249005i	$0.919897\pi$
$548$	3.34552	+	2.55446i	0.142914	+	0.109121i
$549$	−8.50384	−	16.1089i	−0.362935	−	0.687511i
$550$	18.6215	−	0.288883i	0.794024	−	0.0123180i
$551$		−	3.20052i		−	0.136347i
$552$	10.0515	−	28.1806i	0.427819	−	1.19945i
$553$	−1.47586	−	1.47586i	−0.0627597	−	0.0627597i
$554$	11.5833	−	13.2401i	0.492129	−	0.562517i
$555$	3.33167	+	15.0906i	0.141422	+	0.640559i
$556$	−26.3696	+	3.53561i	−1.11832	+	0.149943i
$557$	15.9467	−	15.9467i	0.675684	−	0.675684i	−0.283337	−	0.959020i	$-0.591441\pi$
$557$	15.9467	−	15.9467i	0.675684	−	0.675684i	0.959020	+	0.283337i	$0.0914414\pi$
$558$	8.32098	+	13.5003i	0.352255	+	0.571515i
$559$			52.9651i			2.24019i
$560$	1.09287	+	4.44651i	0.0461820	+	0.187899i
$561$	−12.0361	+	19.9641i	−0.508165	+	0.842884i
$562$	−0.692584	+	0.0462237i	−0.0292149	+	0.00194983i
$563$	−2.27954	−	2.27954i	−0.0960712	−	0.0960712i	0.657438	−	0.753509i	$-0.271640\pi$
$563$	−2.27954	−	2.27954i	−0.0960712	−	0.0960712i	−0.753509	+	0.657438i	$0.771640\pi$
$564$	−1.92514	+	4.43839i	−0.0810631	+	0.186890i
$565$	0.354273	−	13.8547i	0.0149044	−	0.582874i
$566$	−14.2052	−	12.4277i	−0.597089	−	0.522375i
$567$	0.852186	+	4.52787i	0.0357885	+	0.190153i
$568$	−23.9426	+	4.85156i	−1.00461	+	0.203567i
$569$	−38.0835			−1.59654			−0.798272	−	0.602297i	$-0.794252\pi$
$569$	−38.0835			−1.59654			−0.798272	+	0.602297i	$0.794252\pi$
$570$	1.77004	−	3.22880i	0.0741390	−	0.135240i
$571$			39.4382i			1.65044i	0.564815	+	0.825218i	$0.308948\pi$
$571$			39.4382i			1.65044i	−0.564815	+	0.825218i	$0.691052\pi$
$572$	15.7948	−	20.6861i	0.660414	−	0.864931i
$573$	−37.7429	+	9.35070i	−1.57673	+	0.390631i
$574$	−1.95461	+	2.23417i	−0.0815839	+	0.0932526i
$575$	−20.4608	−	22.6679i	−0.853274	−	0.945316i
$576$	15.1884	−	18.5826i	0.632850	−	0.774275i
$577$	15.6617	−	15.6617i	0.652007	−	0.652007i	−0.301469	−	0.953476i	$-0.597477\pi$
$577$	15.6617	−	15.6617i	0.652007	−	0.652007i	0.953476	+	0.301469i	$0.0974770\pi$
$578$	12.8594	−	0.858246i	0.534879	−	0.0356983i
$579$	10.1353	−	16.8112i	0.421208	−	0.698650i
$580$	−16.5863	−	13.3491i	−0.688708	−	0.554293i
$581$	−6.18200			−0.256473
$582$	1.04881	−	2.03490i	0.0434744	−	0.0843494i
$583$	1.70183	+	1.70183i	0.0704824	+	0.0704824i
$584$	25.0348	−	37.7589i	1.03595	−	1.56248i
$585$	14.7190	+	29.6972i	0.608556	+	1.22783i
$586$	−5.28492	+	6.04081i	−0.218318	+	0.249544i
$587$	−8.03380	+	8.03380i	−0.331590	+	0.331590i	−0.853190	−	0.521600i	$-0.825335\pi$
$587$	−8.03380	+	8.03380i	−0.331590	+	0.331590i	0.521600	+	0.853190i	$0.325335\pi$
$588$	−21.7091	+	8.57391i	−0.895267	+	0.353582i
$589$	−2.51288			−0.103541
$590$	−10.5457	+	11.4497i	−0.434159	+	0.471377i
$591$	−3.14255	−	1.89461i	−0.129267	−	0.0779338i
$592$	−13.8604	−	7.91438i	−0.569657	−	0.325279i
$593$	−15.7097	+	15.7097i	−0.645122	+	0.645122i	−0.951810	−	0.306688i	$-0.900779\pi$
$593$	−15.7097	+	15.7097i	−0.645122	+	0.645122i	0.306688	+	0.951810i	$0.400779\pi$
$594$	−13.5506	+	13.8193i	−0.555988	+	0.567013i
$595$	−4.24067	+	4.02920i	−0.173850	+	0.165181i
$596$	−1.38860	−	10.3566i	−0.0568793	−	0.424222i
$597$	−21.2104	+	5.25482i	−0.868083	+	0.215066i
$598$	−42.5801	+	2.84184i	−1.74123	+	0.116211i
$599$	−16.2242			−0.662902			−0.331451	−	0.943473i	$-0.607538\pi$
$599$	−16.2242			−0.662902			−0.331451	+	0.943473i	$0.607538\pi$
$600$	−9.35014	−	22.6401i	−0.381718	−	0.924279i
$601$	30.2446			1.23370			0.616852	−	0.787079i	$-0.288408\pi$
$601$	30.2446			1.23370			0.616852	+	0.787079i	$0.288408\pi$
$602$	−7.74359	+	0.516815i	−0.315605	+	0.0210638i
$603$	1.41503	+	0.437230i	0.0576247	+	0.0178054i
$604$	23.4920	−	3.14978i	0.955875	−	0.128163i
$605$	−6.58648	+	6.25804i	−0.267778	+	0.254425i
$606$	8.09238	−	2.58775i	0.328730	−	0.105120i
$607$	26.6799	−	26.6799i	1.08290	−	1.08290i	0.0866645	−	0.996238i	$-0.472379\pi$
$607$	26.6799	−	26.6799i	1.08290	−	1.08290i	0.996238	−	0.0866645i	$-0.0276208\pi$
$608$	1.24385	+	3.59374i	0.0504448	+	0.145745i
$609$	−2.17954	+	3.61516i	−0.0883194	+	0.146494i
$610$	13.0082	−	14.1233i	0.526686	−	0.571835i
$611$	6.90044			0.279162
$612$	30.2371	+	5.07837i	1.22226	+	0.205281i
$613$	11.2416	−	11.2416i	0.454046	−	0.454046i	−0.442649	−	0.896695i	$-0.645961\pi$
$613$	11.2416	−	11.2416i	0.454046	−	0.454046i	0.896695	+	0.442649i	$0.145961\pi$
$614$	10.5469	−	12.0554i	0.425637	−	0.486515i
$615$	8.54416	−	13.3858i	0.344534	−	0.539769i
$616$	3.17847	+	2.10738i	0.128064	+	0.0849088i
$617$	−15.8402	−	15.8402i	−0.637702	−	0.637702i	0.312286	−	0.949988i	$-0.398905\pi$
$617$	−15.8402	−	15.8402i	−0.637702	−	0.637702i	−0.949988	+	0.312286i	$0.898905\pi$
$618$	−26.7521	−	13.7882i	−1.07613	−	0.554645i
$619$	−39.2267			−1.57665			−0.788327	−	0.615256i	$-0.789052\pi$
$619$	−39.2267			−1.57665			−0.788327	+	0.615256i	$0.789052\pi$
$620$	−10.4810	+	13.0227i	−0.420928	+	0.523003i
$621$	31.6832	+	1.80234i	1.27140	+	0.0723254i
$622$	−18.1851	+	1.21369i	−0.729156	+	0.0486645i
$623$	2.38400	−	2.38400i	0.0955130	−	0.0955130i
$624$	−32.9364	−	9.32754i	−1.31851	−	0.373401i
$625$	−24.8694	−	2.55204i	−0.994776	−	0.102082i
$626$	16.1966	−	18.5132i	0.647346	−	0.739935i
$627$	−0.737493	−	2.97679i	−0.0294526	−	0.118882i
$628$	31.3652	+	23.9487i	1.25161	+	0.955658i
$629$		−	20.3903i		−	0.813016i
$630$	−4.19816	+	2.44172i	−0.167259	+	0.0972804i
$631$	9.52029			0.378997			0.189498	−	0.981881i	$-0.439314\pi$
$631$	9.52029			0.378997			0.189498	+	0.981881i	$0.439314\pi$
$632$	−11.3020	+	2.29016i	−0.449569	+	0.0910977i
$633$	23.5387	−	5.83166i	0.935580	−	0.231788i
$634$	−13.9112	−	12.1705i	−0.552483	−	0.483350i
$635$	0.799214	−	31.2553i	0.0317158	−	1.24033i
$636$	1.25963	−	2.90406i	0.0499475	−	0.115153i
$637$	23.5407	+	23.5407i	0.932717	+	0.932717i
$638$	−17.6934	+	1.18088i	−0.700489	+	0.0467513i
$639$	−12.0963	−	22.9142i	−0.478524	−	0.906472i
$640$	23.8121	+	8.54312i	0.941255	+	0.337696i
$641$			42.2578i			1.66908i	0.550945	+	0.834541i	$0.314267\pi$
$641$			42.2578i			1.66908i	−0.550945	+	0.834541i	$0.685733\pi$
$642$	−4.93515	+	9.57522i	−0.194775	+	0.377904i
$643$	15.1060	−	15.1060i	0.595722	−	0.595722i	−0.343449	−	0.939171i	$-0.611595\pi$
$643$	15.1060	−	15.1060i	0.595722	−	0.595722i	0.939171	+	0.343449i	$0.111595\pi$
$644$	−0.830963	−	6.19756i	−0.0327445	−	0.244218i
$645$	40.5409	−	8.95055i	1.59630	−	0.352428i
$646$	−3.19895	+	3.65649i	−0.125861	+	0.143863i
$647$	−11.1088	−	11.1088i	−0.436732	−	0.436732i	0.454178	−	0.890911i	$-0.349933\pi$
$647$	−11.1088	−	11.1088i	−0.436732	−	0.436732i	−0.890911	+	0.454178i	$0.849933\pi$
$648$	23.4519	+	9.89982i	0.921279	+	0.388902i
$649$			12.9648i			0.508912i
$650$	−24.3184	+	25.0849i	−0.953848	+	0.983909i
$651$	2.83843	+	1.71126i	0.111247	+	0.0670695i
$652$	11.4392	−	14.9817i	0.447995	−	0.586729i
$653$	−15.4673	−	15.4673i	−0.605283	−	0.605283i	0.336426	−	0.941710i	$-0.390782\pi$
$653$	−15.4673	−	15.4673i	−0.605283	−	0.605283i	−0.941710	+	0.336426i	$0.890782\pi$
$654$	−9.66651	+	3.09112i	−0.377991	+	0.120872i
$655$	−14.2564	+	13.5455i	−0.557044	+	0.529267i
$656$	4.32042	+	15.8218i	0.168684	+	0.617738i
$657$	45.9108	+	14.1859i	1.79115	+	0.553445i
$658$	0.0673320	+	1.00886i	0.00262487	+	0.0393293i
$659$			5.93274i			0.231107i	0.993301	+	0.115553i	$0.0368641\pi$
$659$			5.93274i			0.231107i	−0.993301	+	0.115553i	$0.963136\pi$
$660$	−18.5029	−	8.59401i	−0.720223	−	0.334521i
$661$		−	28.1054i		−	1.09317i	−0.837403	−	0.546586i	$-0.815927\pi$
$661$		−	28.1054i		−	1.09317i	0.837403	−	0.546586i	$-0.184073\pi$
$662$	−31.3760	+	2.09406i	−1.21946	+	0.0813881i
$663$	−10.5165	−	42.4486i	−0.408429	−	1.64857i
$664$	−18.8742	+	28.4671i	−0.732461	+	1.10474i
$665$	0.0196714	−	0.769298i	0.000762823	−	0.0298321i
$666$	3.90953	−	16.4714i	0.151491	−	0.638252i
$667$	20.5596	+	20.5596i	0.796069	+	0.796069i
$668$	35.1719	+	26.8553i	1.36084	+	1.03906i
$669$	−3.24434	+	5.38133i	−0.125433	+	0.208054i
$670$	0.0641098	+	1.55984i	0.00247678	+	0.0602619i
$671$		−	15.9922i		−	0.617370i
$672$	1.04232	−	4.90638i	0.0402084	−	0.189268i
$673$	−15.2277	−	15.2277i	−0.586986	−	0.586986i	0.349828	−	0.936814i	$-0.386240\pi$
$673$	−15.2277	−	15.2277i	−0.586986	−	0.586986i	−0.936814	+	0.349828i	$0.886240\pi$
$674$	13.5276	+	11.8349i	0.521063	+	0.455862i
$675$	20.2436	−	16.2848i	0.779178	−	0.626803i
$676$	3.03327	+	22.6230i	0.116664	+	0.870116i
$677$	−28.2327	+	28.2327i	−1.08507	+	1.08507i	−0.0890415	+	0.996028i	$0.528380\pi$
$677$	−28.2327	+	28.2327i	−1.08507	+	1.08507i	−0.996028	+	0.0890415i	$0.971620\pi$
$678$	−6.95547	+	13.4951i	−0.267123	+	0.518275i
$679$		−	0.478448i		−	0.0183611i
$680$	5.60670	+	31.8291i	0.215007	+	1.22059i
$681$	28.0352	+	16.9021i	1.07431	+	0.647691i
$682$	0.927161	+	13.8919i	0.0355028	+	0.531950i
$683$	−26.1080	−	26.1080i	−0.998996	−	0.998996i	0.00100333	−	0.999999i	$-0.499681\pi$
$683$	−26.1080	−	26.1080i	−0.998996	−	0.998996i	−0.999999	+	0.00100333i	$0.999681\pi$
$684$	−3.28520	+	2.34037i	−0.125613	+	0.0894865i
$685$	−4.70454	−	0.120298i	−0.179751	−	0.00459634i
$686$	−6.54891	+	7.48559i	−0.250039	+	0.285801i
$687$	6.56460	+	26.4971i	0.250455	+	1.01093i
$688$	−21.2620	+	37.2359i	−0.810607	+	1.41961i
$689$	−4.51498			−0.172007
$690$	9.37081	+	32.1117i	0.356741	+	1.22247i
$691$		−	9.65683i		−	0.367363i	−0.982986	−	0.183682i	$-0.941198\pi$
$691$		−	9.65683i		−	0.367363i	0.982986	−	0.183682i	$-0.0588015\pi$
$692$	14.3949	+	10.9912i	0.547213	+	0.417822i
$693$	−1.19414	+	3.86468i	−0.0453617	+	0.146807i
$694$	−13.9310	−	12.1878i	−0.528814	−	0.462643i
$695$	21.5643	−	20.4890i	0.817982	−	0.777192i
$696$	9.99292	+	21.0738i	0.378781	+	0.798802i
$697$	−14.8159	+	14.8159i	−0.561191	+	0.561191i
$698$	−1.65674	−	24.8234i	−0.0627085	−	0.939580i
$699$	27.3120	+	16.4661i	1.03303	+	0.622804i
$700$	−3.90474	−	3.31063i	−0.147585	−	0.125130i
$701$	22.2509			0.840403			0.420202	−	0.907431i	$-0.361959\pi$
$701$	22.2509			0.840403			0.420202	+	0.907431i	$0.361959\pi$
$702$	−0.356434	−	36.3065i	−0.0134527	−	1.37030i
$703$	1.89679	+	1.89679i	0.0715390	+	0.0715390i
$704$	19.4083	−	8.20233i	0.731478	−	0.309137i
$705$	−1.16610	−	5.28177i	−0.0439179	−	0.198923i
$706$	−19.5161	−	17.0741i	−0.734499	−	0.642591i
$707$	1.25556	−	1.25556i	0.0472202	−	0.0472202i
$708$	15.8598	−	6.26377i	0.596048	−	0.235407i
$709$	22.1309			0.831144			0.415572	−	0.909560i	$-0.363581\pi$
$709$	22.1309			0.831144			0.415572	+	0.909560i	$0.363581\pi$
$710$	18.5036	−	20.0898i	0.694427	−	0.753956i
$711$	−5.71003	−	10.8166i	−0.214143	−	0.405653i
$712$	−3.69938	−	18.2565i	−0.138640	−	0.684192i
$713$	16.1423	−	16.1423i	0.604533	−	0.604533i
$714$	6.10344	−	1.95173i	0.228416	−	0.0730418i
$715$	−0.743829	+	29.0893i	−0.0278176	+	1.08788i
$716$	0.154823	+	1.15472i	0.00578602	+	0.0431538i
$717$	−10.3437	−	41.7509i	−0.386292	−	1.55922i
$718$	−1.55621	−	23.3172i	−0.0580772	−	0.870189i
$719$	4.65932			0.173763			0.0868817	−	0.996219i	$-0.472310\pi$
$719$	4.65932			0.173763			0.0868817	+	0.996219i	$0.472310\pi$
$720$	−1.57363	+	26.7866i	−0.0586457	+	0.998279i
$721$	−6.28997			−0.234251
$722$	1.74679	+	26.1727i	0.0650088	+	0.974047i
$723$	−7.20539	−	29.0836i	−0.267971	−	1.08163i
$724$	−0.987182	−	7.36268i	−0.0366883	−	0.273632i
$725$	23.7729	+	1.21657i	0.882903	+	0.0451821i
$726$	9.47968	−	3.03138i	0.351824	−	0.112505i
$727$	−28.8504	+	28.8504i	−1.07000	+	1.07000i	−0.0726443	+	0.997358i	$0.523144\pi$
$727$	−28.8504	+	28.8504i	−1.07000	+	1.07000i	−0.997358	+	0.0726443i	$0.976856\pi$
$728$	−7.01174	+	1.42081i	−0.259872	+	0.0526588i
$729$	−3.06195	+	26.8258i	−0.113406	+	0.993549i
$730$	2.08004	+	50.6090i	0.0769858	+	1.87312i
$731$	−54.7787			−2.02606
$732$	−19.5632	+	7.72641i	−0.723077	+	0.285576i
$733$	23.8359	−	23.8359i	0.880398	−	0.880398i	−0.113177	−	0.993575i	$-0.536103\pi$
$733$	23.8359	−	23.8359i	0.880398	−	0.880398i	0.993575	+	0.113177i	$0.0361026\pi$
$734$	36.8636	+	32.2508i	1.36066	+	1.19040i
$735$	14.0405	−	21.9968i	0.517893	−	0.811364i
$736$	−31.0758	−	15.0952i	−1.14547	−	0.556418i
$737$	0.919420	+	0.919420i	0.0338673	+	0.0338673i
$738$	−14.8090	+	9.12759i	−0.545128	+	0.335991i
$739$	29.6476			1.09060			0.545302	−	0.838240i	$-0.316415\pi$
$739$	29.6476			1.09060			0.545302	+	0.838240i	$0.316415\pi$
$740$	17.7413	−	1.91850i	0.652182	−	0.0705256i
$741$	4.92704	+	2.97046i	0.180999	+	0.109122i
$742$	−0.0440556	−	0.660098i	−0.00161733	−	0.0242330i
$743$	−8.41878	+	8.41878i	−0.308855	+	0.308855i	−0.844465	−	0.535610i	$-0.820082\pi$
$743$	−8.41878	+	8.41878i	−0.308855	+	0.308855i	0.535610	+	0.844465i	$0.320082\pi$
$744$	16.5461	−	7.84591i	0.606608	−	0.287645i
$745$	8.04699	+	8.46932i	0.294819	+	0.310292i
$746$	−0.611258	−	0.534771i	−0.0223797	−	0.0195793i
$747$	−34.6130	−	10.6950i	−1.26642	−	0.391310i
$748$	21.3945	+	16.3356i	0.782259	+	0.597290i
$749$			2.25134i			0.0822620i
$750$	23.3101	+	14.3749i	0.851166	+	0.524896i
$751$	−31.5577			−1.15156			−0.575778	−	0.817606i	$-0.695301\pi$
$751$	−31.5577			−1.15156			−0.575778	+	0.817606i	$0.695301\pi$
$752$	4.85119	+	2.77007i	0.176905	+	0.101014i
$753$	0.437480	+	1.76583i	0.0159426	+	0.0643503i
$754$	21.9041	−	25.0370i	0.797700	−	0.911793i
$755$	−19.2111	+	18.2531i	−0.699163	+	0.664299i
$756$	5.30459	−	0.406377i	0.192926	−	0.0147798i
$757$	25.5118	+	25.5118i	0.927244	+	0.927244i	0.997527	−	0.0702832i	$-0.0223903\pi$
$757$	25.5118	+	25.5118i	0.927244	+	0.927244i	−0.0702832	+	0.997527i	$0.522390\pi$
$758$	−0.539733	−	8.08698i	−0.0196040	−	0.293732i
$759$	23.8599	+	14.3848i	0.866059	+	0.522137i
$760$	−3.48244	−	2.43932i	−0.126321	−	0.0884834i
$761$			2.30287i			0.0834789i	0.999129	+	0.0417394i	$0.0132899\pi$
$761$			2.30287i			0.0834789i	−0.999129	+	0.0417394i	$0.986710\pi$
$762$	−15.6910	+	30.4439i	−0.568426	+	1.10286i
$763$	−1.49979	+	1.49979i	−0.0542962	+	0.0542962i
$764$	5.96666	+	44.5011i	0.215866	+	1.60999i
$765$	−30.7141	+	15.2230i	−1.11047	+	0.550389i
$766$	25.9810	+	22.7300i	0.938733	+	0.821269i
$767$	−17.1979	−	17.1979i	−0.620981	−	0.620981i
$768$	−19.4108	−	19.7793i	−0.700426	−	0.713725i
$769$		−	46.5571i		−	1.67889i	−0.543442	−	0.839447i	$-0.682879\pi$
$769$		−	46.5571i		−	1.67889i	0.543442	−	0.839447i	$-0.317121\pi$
$770$	−4.26016	+	0.175094i	−0.153526	+	0.00630994i
$771$	2.78633	−	4.62164i	0.100347	−	0.166444i
$772$	−18.0157	−	13.7558i	−0.648399	−	0.495082i
$773$	19.2506	+	19.2506i	0.692397	+	0.692397i	0.962759	−	0.270362i	$-0.0871434\pi$
$773$	19.2506	+	19.2506i	0.692397	+	0.692397i	−0.270362	+	0.962759i	$0.587143\pi$
$774$	−44.2504	−	10.5030i	−1.59055	−	0.377521i
$775$	0.955183	−	18.6652i	0.0343112	−	0.670474i
$776$	−2.20318	−	1.46074i	−0.0790894	−	0.0524377i
$777$	−0.850825	−	3.43424i	−0.0305232	−	0.123203i
$778$	−39.4113	+	2.63035i	−1.41296	+	0.0943024i
$779$		−	2.75647i		−	0.0987608i
$780$	35.9443	−	13.1442i	1.28701	−	0.470638i
$781$		−	22.7481i		−	0.813993i
$782$	−2.93914	−	44.0381i	−0.105104	−	1.57480i
$783$	−18.4575	+	16.4706i	−0.659618	+	0.588611i
$784$	7.09969	+	25.9998i	0.253560	+	0.928564i
$785$	−44.1064	−	1.12782i	−1.57422	−	0.0402537i
$786$	20.5188	−	6.56141i	0.731880	−	0.234038i
$787$	3.79411	+	3.79411i	0.135246	+	0.135246i	0.771489	−	0.636243i	$-0.219512\pi$
$787$	3.79411	+	3.79411i	0.135246	+	0.135246i	−0.636243	+	0.771489i	$0.719512\pi$
$788$	−2.57140	+	3.36771i	−0.0916023	+	0.119970i
$789$	−15.7317	−	9.48447i	−0.560064	−	0.337656i
$790$	8.73453	−	9.48329i	0.310761	−	0.337400i
$791$			3.17297i			0.112818i
$792$	14.1504	+	17.2980i	0.502812	+	0.614659i
$793$	21.2138	+	21.2138i	0.753324	+	0.753324i
$794$	4.16445	−	4.76008i	0.147791	−	0.168929i
$795$	0.762985	+	3.45588i	0.0270603	+	0.122568i
$796$	3.35309	+	25.0083i	0.118847	+	0.886396i
$797$	30.0747	−	30.0747i	1.06530	−	1.06530i	0.0675880	−	0.997713i	$-0.478470\pi$
$797$	30.0747	−	30.0747i	1.06530	−	1.06530i	0.997713	−	0.0675880i	$-0.0215303\pi$
$798$	−0.386209	+	0.749327i	−0.0136717	+	0.0265259i
$799$			7.13671i			0.252479i
$800$	−27.1664	+	7.87306i	−0.960478	+	0.278355i
$801$	17.4724	−	9.22362i	0.617356	−	0.325901i
$802$	−15.8789	+	1.05977i	−0.560702	+	0.0374218i
$803$	29.8306	+	29.8306i	1.05270	+	1.05270i
$804$	0.680520	−	1.56893i	0.0240001	−	0.0553320i
$805$	4.81546	+	5.06819i	0.169723	+	0.178630i
$806$	−19.6577	−	17.1979i	−0.692413	−	0.605771i
$807$	35.6407	−	8.82990i	1.25461	−	0.310827i
$808$	−1.94832	−	9.61499i	−0.0685416	−	0.338254i
$809$	21.7890			0.766061			0.383031	−	0.923736i	$-0.374880\pi$
$809$	21.7890			0.766061			0.383031	+	0.923736i	$0.374880\pi$
$810$	−27.7297	+	6.40824i	−0.974321	+	0.225162i
$811$			2.48698i			0.0873295i	0.999046	+	0.0436648i	$0.0139033\pi$
$811$			2.48698i			0.0873295i	−0.999046	+	0.0436648i	$0.986097\pi$
$812$	3.87418	+	2.95811i	0.135957	+	0.103809i
$813$	6.11234	+	24.6716i	0.214369	+	0.865272i
$814$	9.78619	−	11.1859i	0.343006	−	0.392065i
$815$	−0.538710	+	21.0676i	−0.0188702	+	0.737966i
$816$	9.64692	−	34.0642i	0.337710	−	1.19249i
$817$	5.09575	−	5.09575i	0.178278	−	0.178278i
$818$	7.13954	−	0.476499i	0.249628	−	0.0166604i
$819$	−3.54250	−	6.71058i	−0.123785	−	0.234487i
$820$	−14.2851	−	11.4970i	−0.498856	−	0.401494i
$821$	−7.50855			−0.262050			−0.131025	−	0.991379i	$-0.541827\pi$
$821$	−7.50855			−0.262050			−0.131025	+	0.991379i	$0.541827\pi$
$822$	4.58241	+	2.36181i	0.159830	+	0.0823777i
$823$	33.8234	+	33.8234i	1.17901	+	1.17901i	0.979997	+	0.199012i	$0.0637733\pi$
$823$	33.8234	+	33.8234i	1.17901	+	1.17901i	0.199012	+	0.979997i	$0.436227\pi$
$824$	−19.2038	+	28.9643i	−0.668997	+	1.00902i
$825$	22.3914	−	4.34644i	0.779568	−	0.151324i
$826$	2.34656	−	2.68218i	0.0816471	−	0.0933249i
$827$	20.6186	−	20.6186i	0.716979	−	0.716979i	−0.251007	−	0.967985i	$-0.580762\pi$
$827$	20.6186	−	20.6186i	0.716979	−	0.716979i	0.967985	+	0.251007i	$0.0807616\pi$
$828$	6.06937	−	36.1376i	0.210925	−	1.25587i
$829$	16.9499			0.588694			0.294347	−	0.955699i	$-0.404898\pi$
$829$	16.9499			0.588694			0.294347	+	0.955699i	$0.404898\pi$
$830$	−1.56818	−	38.1551i	−0.0544324	−	1.32438i
$831$	11.1243	−	18.4516i	0.385896	−	0.640079i
$832$	−14.8649	+	36.6258i	−0.515346	+	1.26977i
$833$	−24.3468	+	24.3468i	−0.843565	+	0.843565i
$834$	−31.0368	+	9.92482i	−1.07472	+	0.343668i
$835$	−49.4594	−	1.26470i	−1.71161	−	0.0437669i
$836$	−3.50981	+	0.470593i	−0.121389	+	0.0162758i
$837$	12.9318	+	14.4919i	0.446990	+	0.500912i
$838$	35.5340	−	2.37157i	1.22750	−	0.0819246i
$839$	−31.3869			−1.08360			−0.541798	−	0.840509i	$-0.682256\pi$
$839$	−31.3869			−1.08360			−0.541798	+	0.840509i	$0.682256\pi$
$840$	2.27244	+	5.12686i	0.0784065	+	0.176894i
$841$	6.33479			0.218441
$842$	44.4617	−	2.96742i	1.53225	−	0.102264i
$843$	−0.825179	+	0.204436i	−0.0284207	+	0.00704116i
$844$	−3.72117	−	27.7535i	−0.128088	−	0.955316i
$845$	−17.5780	−	18.5005i	−0.604700	−	0.636436i
$846$	−1.36835	+	5.76506i	−0.0470450	+	0.198207i
$847$	1.47081	−	1.47081i	0.0505375	−	0.0505375i
$848$	−3.17415	−	1.81247i	−0.109001	−	0.0622405i
$849$	−19.7966	−	11.9351i	−0.679418	−	0.409613i
$850$	−25.9438	−	25.1511i	−0.889864	−	0.862676i
$851$	−24.3693			−0.835369
$852$	−27.8278	+	10.9905i	−0.953365	+	0.376528i
$853$	−4.93576	+	4.93576i	−0.168997	+	0.168997i	−0.786538	−	0.617541i	$-0.788129\pi$
$853$	−4.93576	+	4.93576i	−0.168997	+	0.168997i	0.617541	+	0.786538i	$0.288129\pi$
$854$	−2.89449	+	3.30849i	−0.0990476	+	0.113214i
$855$	1.44104	−	4.27326i	0.0492827	−	0.146142i
$856$	10.3670	+	6.87353i	0.354338	+	0.234932i
$857$	23.9182	+	23.9182i	0.817029	+	0.817029i	0.985676	−	0.168648i	$-0.0539400\pi$
$857$	23.9182	+	23.9182i	0.817029	+	0.817029i	−0.168648	+	0.985676i	$0.553940\pi$
$858$	14.6037	−	28.3341i	0.498560	−	0.967311i
$859$	−22.2708			−0.759871			−0.379935	−	0.925013i	$-0.624054\pi$
$859$	−22.2708			−0.759871			−0.379935	+	0.925013i	$0.624054\pi$
$860$	−5.15407	−	47.6620i	−0.175752	−	1.62526i
$861$	−1.87714	+	3.11358i	−0.0639728	+	0.106111i
$862$	19.2021	−	1.28157i	0.654027	−	0.0436503i
$863$	37.8907	−	37.8907i	1.28982	−	1.28982i	0.354918	−	0.934897i	$-0.384509\pi$
$863$	37.8907	−	37.8907i	1.28982	−	1.28982i	0.934897	−	0.354918i	$-0.115491\pi$
$864$	14.3241	−	25.6675i	0.487315	−	0.873226i
$865$	−20.2425	−	0.517611i	−0.688265	−	0.0175993i
$866$	3.70706	−	4.23727i	0.125971	−	0.143988i
$867$	15.3213	−	3.79581i	0.520338	−	0.128912i
$868$	2.32255	−	3.04180i	0.0788326	−	0.103245i
$869$		−	10.7382i		−	0.364267i
$870$	−22.8655	−	12.5350i	−0.775213	−	0.424975i
$871$	−2.43924			−0.0826506
$872$	2.32731	+	11.4853i	0.0788125	+	0.388942i
$873$	0.827726	−	2.67882i	0.0280143	−	0.0906645i
$874$	4.37002	+	3.82320i	0.147818	+	0.129322i
$875$	5.70673	+	0.438537i	0.192923	+	0.0148253i
$876$	22.0795	−	50.9040i	0.745996	−	1.71989i
$877$	−19.4977	−	19.4977i	−0.658392	−	0.658392i	0.296608	−	0.954999i	$-0.404145\pi$
$877$	−19.4977	−	19.4977i	−0.658392	−	0.658392i	−0.954999	+	0.296608i	$0.904145\pi$
$878$	7.85403	−	0.524185i	0.265061	−	0.0176904i
$879$	−5.07546	+	8.41857i	−0.171191	+	0.283951i
$880$	−12.2004	+	20.1520i	−0.411275	+	0.679322i
$881$		−	36.8489i		−	1.24147i	−0.784021	−	0.620735i	$-0.786834\pi$
$881$		−	36.8489i		−	1.24147i	0.784021	−	0.620735i	$-0.213166\pi$
$882$	−24.3355	+	14.9993i	−0.819419	+	0.505052i
$883$	−25.6982	+	25.6982i	−0.864813	+	0.864813i	−0.991893	−	0.127079i	$-0.959440\pi$
$883$	−25.6982	+	25.6982i	−0.864813	+	0.864813i	0.127079	+	0.991893i	$0.459440\pi$
$884$	−50.0494	+	6.71058i	−1.68334	+	0.225701i
$885$	−10.2575	+	16.0700i	−0.344801	+	0.540187i
$886$	−4.65458	+	5.32031i	−0.156374	+	0.178739i
$887$	19.3369	+	19.3369i	0.649270	+	0.649270i	0.952817	−	0.303547i	$-0.0981709\pi$
$887$	19.3369	+	19.3369i	0.649270	+	0.649270i	−0.303547	+	0.952817i	$0.598171\pi$
$888$	−18.4118	−	6.56712i	−0.617858	−	0.220378i
$889$			7.15799i			0.240071i
$890$	15.3187	+	14.1092i	0.513484	+	0.472942i
$891$	−13.3720	+	19.5724i	−0.447978	+	0.655699i
$892$	5.76689	+	4.40328i	0.193090	+	0.147433i
$893$	−0.663887	−	0.663887i	−0.0222161	−	0.0222161i
$894$	−3.89794	−	12.1896i	−0.130367	−	0.407681i
$895$	−0.897207	−	0.944295i	−0.0299903	−	0.0315643i
$896$	−5.49980	−	1.81589i	−0.183736	−	0.0606645i
$897$	−50.7321	+	12.5688i	−1.69389	+	0.419658i
$898$	1.99555	+	29.9000i	0.0665925	+	0.997775i
$899$			17.7955i			0.593514i
$900$	−16.1351	−	25.2915i	−0.537837	−	0.843049i
$901$		−	4.66958i		−	0.155566i
$902$	−15.2386	+	1.01704i	−0.507389	+	0.0338636i
$903$	−9.22610	+	2.28574i	−0.307025	+	0.0760648i
$904$	14.6110	+	9.68737i	0.485956	+	0.322197i
$905$	5.72076	+	6.02100i	0.190164	+	0.200145i
$906$	27.6499	−	8.84176i	0.918605	−	0.293748i
$907$	16.8535	+	16.8535i	0.559613	+	0.559613i	0.929197	−	0.369585i	$-0.120500\pi$
$907$	16.8535	+	16.8535i	0.559613	+	0.559613i	−0.369585	+	0.929197i	$0.620500\pi$
$908$	22.9399	−	30.0439i	0.761287	−	0.997042i
$909$	9.20201	−	4.85772i	0.305212	−	0.161120i
$910$	5.41889	−	5.88342i	0.179635	−	0.195034i
$911$			31.3998i			1.04032i	0.854068	+	0.520161i	$0.174128\pi$
$911$			31.3998i			1.04032i	−0.854068	+	0.520161i	$0.825872\pi$
$912$	2.27140	+	4.06619i	0.0752135	+	0.134645i
$913$	−22.4898	−	22.4898i	−0.744304	−	0.744304i
$914$	−25.4071	−	22.2279i	−0.840393	−	0.735234i
$915$	12.6527	−	19.8225i	0.418284	−	0.655311i
$916$	31.2417	−	4.18886i	1.03225	−	0.138404i
$917$	3.18356	−	3.18356i	0.105130	−	0.105130i
$918$	37.5496	−	0.368638i	1.23932	−	0.0121669i
$919$		−	26.0422i		−	0.859054i	−0.903054	−	0.429527i	$-0.858680\pi$
$919$		−	26.0422i		−	0.859054i	0.903054	−	0.429527i	$-0.141320\pi$
$920$	38.0403	−	6.70079i	1.25415	−	0.220919i
$921$	10.1289	−	16.8006i	0.333757	−	0.553597i
$922$	−0.337986	−	5.06414i	−0.0111310	−	0.166779i
$923$	30.1757	+	30.1757i	0.993245	+	0.993245i
$924$	4.28499	+	1.85860i	0.140966	+	0.0611436i
$925$	−14.8100	+	13.3680i	−0.486951	+	0.439538i
$926$	−34.8972	+	39.8885i	−1.14679	+	1.31082i
$927$	−35.2175	−	10.8818i	−1.15669	−	0.357405i
$928$	25.4499	−	8.80860i	0.835433	−	0.289157i
$929$	16.2184			0.532108			0.266054	−	0.963958i	$-0.414280\pi$
$929$	16.2184			0.532108			0.266054	+	0.963958i	$0.414280\pi$
$930$	−9.84179	+	17.9528i	−0.322725	+	0.588695i
$931$		−	4.52968i		−	0.148454i
$932$	22.3481	−	29.2688i	0.732036	−	0.958733i
$933$	−21.6666	+	5.36785i	−0.709333	+	0.175736i
$934$	31.8871	+	27.8970i	1.04338	+	0.912819i
$935$	−30.0853	−	0.769298i	−0.983896	−	0.0251587i
$936$	−41.7167	−	4.17537i	−1.36355	−	0.136476i
$937$	−14.3578	+	14.3578i	−0.469050	+	0.469050i	−0.901607	−	0.432557i	$-0.857611\pi$
$937$	−14.3578	+	14.3578i	−0.469050	+	0.469050i	0.432557	+	0.901607i	$0.357611\pi$
$938$	−0.0238012	−	0.356621i	−0.000777138	−	0.0116441i
$939$	15.5547	−	25.8002i	0.507607	−	0.841959i
$940$	−6.20953	+	0.671485i	−0.202533	+	0.0219014i
$941$	−27.3264			−0.890817			−0.445408	−	0.895328i	$-0.646941\pi$
$941$	−27.3264			−0.890817			−0.445408	+	0.895328i	$0.646941\pi$
$942$	42.9613	+	22.1426i	1.39976	+	0.721446i
$943$	17.7071	+	17.7071i	0.576621	+	0.576621i
$944$	−5.18676	−	18.9944i	−0.168815	−	0.618216i
$945$	−4.53780	+	3.84553i	−0.147615	+	0.125095i
$946$	−30.0509	−	26.2906i	−0.977040	−	0.854783i
$947$	17.5336	−	17.5336i	0.569766	−	0.569766i	−0.362297	−	0.932063i	$-0.618007\pi$
$947$	17.5336	−	17.5336i	0.569766	−	0.569766i	0.932063	+	0.362297i	$0.118007\pi$
$948$	−13.1360	+	5.18801i	−0.426637	+	0.168499i
$949$	−79.1412			−2.56903
$950$	4.75306	−	0.0737363i	0.154210	−	0.00239232i
$951$	−19.3868	−	11.6881i	−0.628661	−	0.379012i
$952$	−1.46946	−	7.25183i	−0.0476255	−	0.235033i
$953$	19.5859	−	19.5859i	0.634449	−	0.634449i	−0.314732	−	0.949181i	$-0.601915\pi$
$953$	19.5859	−	19.5859i	0.634449	−	0.634449i	0.949181	+	0.314732i	$0.101915\pi$
$954$	0.895319	−	3.77210i	0.0289870	−	0.122126i
$955$	−34.5770	−	36.3917i	−1.11889	−	1.17761i
$956$	−49.2268	+	6.60028i	−1.59211	+	0.213468i
$957$	−21.0808	+	5.22272i	−0.681446	+	0.168827i
$958$	0.243772	+	3.65252i	0.00787593	+	0.118008i
$959$	1.07742			0.0347917
$960$	30.5463	+	5.18856i	0.985879	+	0.167460i
$961$	−17.0279			−0.549287
$962$	1.85671	+	27.8197i	0.0598628	+	0.896943i
$963$	−3.89486	+	12.6052i	−0.125510	+	0.406197i
$964$	−34.2913	+	4.59774i	−1.10445	+	0.148083i
$965$	25.3341	+	0.647805i	0.815532	+	0.0208536i
$966$	−2.33260	−	7.29447i	−0.0750501	−	0.234696i
$967$	−16.0917	+	16.0917i	−0.517475	+	0.517475i	−0.916806	−	0.399332i	$-0.869242\pi$
$967$	−16.0917	+	16.0917i	−0.517475	+	0.517475i	0.399332	+	0.916806i	$0.369242\pi$
$968$	−2.28232	−	11.2633i	−0.0733567	−	0.362017i
$969$	−3.07217	+	5.09575i	−0.0986922	+	0.163699i
$970$	2.95296	−	0.121367i	0.0948138	−	0.00389687i
$971$	56.1374			1.80154			0.900768	−	0.434301i	$-0.143005\pi$
$971$	56.1374			1.80154			0.900768	+	0.434301i	$0.143005\pi$
$972$	30.4034	+	6.90177i	0.975189	+	0.221374i
$973$	−4.81546	+	4.81546i	−0.154377	+	0.154377i
$974$	−12.4932	−	10.9299i	−0.400308	−	0.350217i
$975$	−23.9368	+	35.4681i	−0.766592	+	1.13589i
$976$	6.39791	+	23.4298i	0.204792	+	0.749969i
$977$	−1.50786	−	1.50786i	−0.0482409	−	0.0482409i	0.682575	−	0.730816i	$-0.260860\pi$
$977$	−1.50786	−	1.50786i	−0.0482409	−	0.0482409i	−0.730816	+	0.682575i	$0.760860\pi$
$978$	10.5765	−	20.5207i	0.338200	−	0.656179i
$979$	17.3458			0.554373
$980$	−23.4745	−	18.8929i	−0.749864	−	0.603513i
$981$	−10.9920	+	5.80265i	−0.350948	+	0.185264i
$982$	−2.38928	−	35.7993i	−0.0762450	−	1.14240i
$983$	−20.1605	+	20.1605i	−0.643021	+	0.643021i	−0.951297	−	0.308276i	$-0.900248\pi$
$983$	−20.1605	+	20.1605i	−0.643021	+	0.643021i	0.308276	+	0.951297i	$0.400248\pi$
$984$	8.60647	+	18.1500i	0.274364	+	0.578600i
$985$	0.121096	−	4.73575i	0.00385843	−	0.150893i
$986$	25.8943	+	22.6541i	0.824641	+	0.721454i
$987$	0.297793	+	1.20200i	0.00947885	+	0.0382601i
$988$	4.03156	−	5.28006i	0.128261	−	0.167981i
$989$			65.4683i			2.08177i
$990$	−24.1555	−	6.38984i	−0.767713	−	0.203082i
$991$	36.8471			1.17049			0.585244	−	0.810858i	$-0.300999\pi$
$991$	36.8471			1.17049			0.585244	+	0.810858i	$0.300999\pi$
$992$	−6.91605	−	19.9819i	−0.219585	−	0.634425i
$993$	−37.3829	+	9.26153i	−1.18631	+	0.293906i
$994$	−4.11729	+	4.70618i	−0.130593	+	0.149271i
$995$	−19.4313	−	20.4511i	−0.616013	−	0.648344i
$996$	−16.6461	+	38.3774i	−0.527452	+	1.21604i
$997$	28.1250	+	28.1250i	0.890726	+	0.890726i	0.994591	−	0.103865i	$-0.0331210\pi$
$997$	28.1250	+	28.1250i	0.890726	+	0.890726i	−0.103865	+	0.994591i	$0.533121\pi$
$998$	2.70043	+	40.4614i	0.0854806	+	1.28078i
$999$	1.17756	−	20.7002i	0.0372563	−	0.654926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	120.2.w.c.53.8	yes	32
3.2	odd	2	inner	120.2.w.c.53.9	yes	32
4.3	odd	2		480.2.bi.c.113.10		32
5.2	odd	4	inner	120.2.w.c.77.16	yes	32
5.3	odd	4		600.2.w.j.557.1		32
5.4	even	2		600.2.w.j.293.9		32
8.3	odd	2		480.2.bi.c.113.7		32
8.5	even	2	inner	120.2.w.c.53.1	✓	32
12.11	even	2		480.2.bi.c.113.2		32
15.2	even	4	inner	120.2.w.c.77.1	yes	32
15.8	even	4		600.2.w.j.557.16		32
15.14	odd	2		600.2.w.j.293.8		32
20.7	even	4		480.2.bi.c.17.15		32
24.5	odd	2	inner	120.2.w.c.53.16	yes	32
24.11	even	2		480.2.bi.c.113.15		32
40.13	odd	4		600.2.w.j.557.8		32
40.27	even	4		480.2.bi.c.17.2		32
40.29	even	2		600.2.w.j.293.16		32
40.37	odd	4	inner	120.2.w.c.77.9	yes	32
60.47	odd	4		480.2.bi.c.17.7		32
120.29	odd	2		600.2.w.j.293.1		32
120.53	even	4		600.2.w.j.557.9		32
120.77	even	4	inner	120.2.w.c.77.8	yes	32
120.107	odd	4		480.2.bi.c.17.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.w.c.53.1	✓	32	8.5	even	2	inner
120.2.w.c.53.8	yes	32	1.1	even	1	trivial
120.2.w.c.53.9	yes	32	3.2	odd	2	inner
120.2.w.c.53.16	yes	32	24.5	odd	2	inner
120.2.w.c.77.1	yes	32	15.2	even	4	inner
120.2.w.c.77.8	yes	32	120.77	even	4	inner
120.2.w.c.77.9	yes	32	40.37	odd	4	inner
120.2.w.c.77.16	yes	32	5.2	odd	4	inner
480.2.bi.c.17.2		32	40.27	even	4
480.2.bi.c.17.7		32	60.47	odd	4
480.2.bi.c.17.10		32	120.107	odd	4
480.2.bi.c.17.15		32	20.7	even	4
480.2.bi.c.113.2		32	12.11	even	2
480.2.bi.c.113.7		32	8.3	odd	2
480.2.bi.c.113.10		32	4.3	odd	2
480.2.bi.c.113.15		32	24.11	even	2
600.2.w.j.293.1		32	120.29	odd	2
600.2.w.j.293.8		32	15.14	odd	2
600.2.w.j.293.9		32	5.4	even	2
600.2.w.j.293.16		32	40.29	even	2
600.2.w.j.557.1		32	5.3	odd	4
600.2.w.j.557.8		32	40.13	odd	4
600.2.w.j.557.9		32	120.53	even	4
600.2.w.j.557.16		32	15.8	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0941764 - 1.41107i) q^{2} +(-0.416519 - 1.68122i) q^{3} +(-1.98226 + 0.265780i) q^{4} +(1.62104 - 1.54020i) q^{5} +(-2.33310 + 0.746071i) q^{6} +(-0.361989 + 0.361989i) q^{7} +(0.561717 + 2.77209i) q^{8} +(-2.65302 + 1.40052i) q^{9} +O(q^{10})\)	\(q+(-0.0941764 - 1.41107i) q^{2} +(-0.416519 - 1.68122i) q^{3} +(-1.98226 + 0.265780i) q^{4} +(1.62104 - 1.54020i) q^{5} +(-2.33310 + 0.746071i) q^{6} +(-0.361989 + 0.361989i) q^{7} +(0.561717 + 2.77209i) q^{8} +(-2.65302 + 1.40052i) q^{9} +(-2.32601 - 2.14236i) q^{10} -2.63380 q^{11} +(1.27249 + 3.22192i) q^{12} +(3.49376 - 3.49376i) q^{13} +(0.544885 + 0.476703i) q^{14} +(-3.26462 - 2.08380i) q^{15} +(3.85872 - 1.05369i) q^{16} +(3.61339 + 3.61339i) q^{17} +(2.22609 + 3.61172i) q^{18} -0.672266 q^{19} +(-2.80397 + 3.48393i) q^{20} +(0.759360 + 0.457809i) q^{21} +(0.248041 + 3.71648i) q^{22} +(4.31851 - 4.31851i) q^{23} +(4.42653 - 2.09900i) q^{24} +(0.255538 - 4.99347i) q^{25} +(-5.25899 - 4.60093i) q^{26} +(3.45963 + 3.87698i) q^{27} +(0.621348 - 0.813767i) q^{28} +4.76080i q^{29} +(-2.63295 + 4.80287i) q^{30} +3.73793 q^{31} +(-1.85024 - 5.34571i) q^{32} +(1.09703 + 4.42800i) q^{33} +(4.75847 - 5.43906i) q^{34} +(-0.0292613 + 1.14434i) q^{35} +(4.88676 - 3.48132i) q^{36} +(-2.82150 - 2.82150i) q^{37} +(0.0633116 + 0.948617i) q^{38} +(-7.32901 - 4.41857i) q^{39} +(5.18015 + 3.62850i) q^{40} +4.10027i q^{41} +(0.574489 - 1.11463i) q^{42} +(-7.57996 + 7.57996i) q^{43} +(5.22087 - 0.700010i) q^{44} +(-2.14356 + 6.35650i) q^{45} +(-6.50044 - 5.68704i) q^{46} +(0.987537 + 0.987537i) q^{47} +(-3.37872 - 6.04849i) q^{48} +6.73793i q^{49} +(-7.07022 + 0.109683i) q^{50} +(4.56987 - 7.57996i) q^{51} +(-5.99698 + 7.85412i) q^{52} +(-0.646149 - 0.646149i) q^{53} +(5.14489 - 5.24691i) q^{54} +(-4.26949 + 4.05659i) q^{55} +(-1.20680 - 0.800131i) q^{56} +(0.280012 + 1.13023i) q^{57} +(6.71784 - 0.448355i) q^{58} -4.92247i q^{59} +(7.02517 + 3.26298i) q^{60} +6.07190i q^{61} +(-0.352025 - 5.27449i) q^{62} +(0.453392 - 1.46734i) q^{63} +(-7.36895 + 3.11426i) q^{64} +(0.282417 - 11.0446i) q^{65} +(6.14492 - 1.96500i) q^{66} +(-0.349085 - 0.349085i) q^{67} +(-8.12305 - 6.20232i) q^{68} +(-9.05912 - 5.46164i) q^{69} +(1.61750 - 0.0664796i) q^{70} +8.63702i q^{71} +(-5.37262 - 6.56772i) q^{72} +(-11.3261 - 11.3261i) q^{73} +(-3.71562 + 4.24706i) q^{74} +(-8.50157 + 1.65026i) q^{75} +(1.33261 - 0.178675i) q^{76} +(0.953406 - 0.953406i) q^{77} +(-5.54472 + 10.7579i) q^{78} +4.07707i q^{79} +(4.63224 - 7.65130i) q^{80} +(5.07707 - 7.43124i) q^{81} +(5.78579 - 0.386149i) q^{82} +(8.53893 + 8.53893i) q^{83} +(-1.62693 - 0.705675i) q^{84} +(11.4228 + 0.292087i) q^{85} +(11.4097 + 9.98203i) q^{86} +(8.00397 - 1.98296i) q^{87} +(-1.47945 - 7.30111i) q^{88} -6.58584 q^{89} +(9.17137 + 2.42609i) q^{90} +2.52941i q^{91} +(-7.41264 + 9.70819i) q^{92} +(-1.55692 - 6.28429i) q^{93} +(1.30049 - 1.48649i) q^{94} +(-1.08977 + 1.03543i) q^{95} +(-8.21668 + 5.33725i) q^{96} +(-0.660859 + 0.660859i) q^{97} +(9.50772 - 0.634554i) q^{98} +(6.98752 - 3.68869i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 4 q^{6}+O(q^{10}) \) 32 * q - 4 * q^6	\( 32 q - 4 q^{6} + 4 q^{10} - 8 q^{12} - 28 q^{15} + 28 q^{16} - 20 q^{18} - 52 q^{22} - 8 q^{25} + 12 q^{28} - 32 q^{30} - 32 q^{31} + 8 q^{33} - 20 q^{36} + 24 q^{40} + 16 q^{42} + 24 q^{46} + 44 q^{48} + 8 q^{52} + 8 q^{55} - 16 q^{57} + 28 q^{58} + 56 q^{60} + 48 q^{63} + 16 q^{66} + 20 q^{70} + 32 q^{72} - 64 q^{73} - 88 q^{76} + 64 q^{78} + 48 q^{81} + 64 q^{82} - 8 q^{87} - 52 q^{88} + 84 q^{90} - 52 q^{96} + 16 q^{97}+O(q^{100}) \) 32 * q - 4 * q^6 + 4 * q^10 - 8 * q^12 - 28 * q^15 + 28 * q^16 - 20 * q^18 - 52 * q^22 - 8 * q^25 + 12 * q^28 - 32 * q^30 - 32 * q^31 + 8 * q^33 - 20 * q^36 + 24 * q^40 + 16 * q^42 + 24 * q^46 + 44 * q^48 + 8 * q^52 + 8 * q^55 - 16 * q^57 + 28 * q^58 + 56 * q^60 + 48 * q^63 + 16 * q^66 + 20 * q^70 + 32 * q^72 - 64 * q^73 - 88 * q^76 + 64 * q^78 + 48 * q^81 + 64 * q^82 - 8 * q^87 - 52 * q^88 + 84 * q^90 - 52 * q^96 + 16 * q^97

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