LMFDB - Embedded newform 120.2.w.c.77.16

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			77.16
Character	$\chi$	$=$	120.77
Dual form			120.2.w.c.53.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41107 - 0.0941764i) q^{2} +(-1.68122 + 0.416519i) q^{3} +(1.98226 - 0.265780i) q^{4} +(1.62104 + 1.54020i) q^{5} +(-2.33310 + 0.746071i) q^{6} +(-0.361989 - 0.361989i) q^{7} +(2.77209 - 0.561717i) q^{8} +(2.65302 - 1.40052i) q^{9} +O(q^{10})$	\(q+(1.41107 - 0.0941764i) q^{2} +(-1.68122 + 0.416519i) 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} +(2.77209 - 0.561717i) q^{8} +(2.65302 - 1.40052i) q^{9} +(2.43246 + 2.02068i) q^{10} -2.63380 q^{11} +(-3.22192 + 1.27249i) q^{12} +(-3.49376 - 3.49376i) q^{13} +(-0.544885 - 0.476703i) q^{14} +(-3.36685 - 1.91423i) q^{15} +(3.85872 - 1.05369i) q^{16} +(-3.61339 + 3.61339i) q^{17} +(3.61172 - 2.22609i) q^{18} +0.672266 q^{19} +(3.62268 + 2.62225i) q^{20} +(0.759360 + 0.457809i) q^{21} +(-3.71648 + 0.248041i) 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} +(-3.87698 + 3.45963i) q^{27} +(-0.813767 - 0.621348i) q^{28} -4.76080i q^{29} +(-4.93116 - 2.38405i) q^{30} +3.73793 q^{31} +(5.34571 - 1.85024i) q^{32} +(4.42800 - 1.09703i) 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} +(0.948617 - 0.0633116i) q^{38} +(7.32901 + 4.41857i) q^{39} +(5.35882 + 3.35902i) q^{40} +4.10027i q^{41} +(1.11463 + 0.574489i) q^{42} +(7.57996 + 7.57996i) q^{43} +(-5.22087 + 0.700010i) q^{44} +(6.45775 + 1.81590i) q^{45} +(-6.50044 - 5.68704i) q^{46} +(-0.987537 + 0.987537i) q^{47} +(-6.04849 + 3.37872i) q^{48} -6.73793i q^{49} +(0.830850 + 7.02209i) q^{50} +(4.56987 - 7.57996i) q^{51} +(-7.85412 - 5.99698i) 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} +(-1.13023 + 0.280012i) q^{57} +(-0.448355 - 6.71784i) q^{58} +4.92247i q^{59} +(-7.18275 - 2.89967i) q^{60} +6.07190i q^{61} +(5.27449 - 0.352025i) q^{62} +(-1.46734 - 0.453392i) 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} +(-6.20232 + 8.12305i) q^{68} +(9.05912 + 5.46164i) q^{69} +(-0.149059 - 1.61199i) q^{70} +8.63702i q^{71} +(6.56772 - 5.37262i) q^{72} +(-11.3261 + 11.3261i) q^{73} +(3.71562 - 4.24706i) q^{74} +(-2.50949 - 8.28869i) q^{75} +(1.33261 - 0.178675i) q^{76} +(0.953406 + 0.953406i) q^{77} +(10.7579 + 5.54472i) q^{78} -4.07707i q^{79} +(7.87804 + 4.23515i) q^{80} +(5.07707 - 7.43124i) q^{81} +(0.386149 + 5.78579i) 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} +(1.98296 + 8.00397i) q^{87} +(-7.30111 + 1.47945i) q^{88} +6.58584 q^{89} +(9.28338 + 1.95420i) q^{90} +2.52941i q^{91} +(-9.70819 - 7.41264i) q^{92} +(-6.28429 + 1.55692i) 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} +(-0.634554 - 9.50772i) 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 $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.41107	−	0.0941764i	0.997780	−	0.0665928i
$2$	1.41107	−	0.0941764i	0.997780	−	0.0665928i
$3$	−1.68122	+	0.416519i	−0.970655	+	0.240477i
$3$	−1.68122	+	0.416519i	−0.970655	+	0.240477i
$4$	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	0.635380	−	0.772199i	$-0.280843\pi$
$7$	−0.361989	−	0.361989i	−0.136819	−	0.136819i	−0.772199	+	0.635380i	$0.780843\pi$
$8$	2.77209	−	0.561717i	0.980081	−	0.198597i
$9$	2.65302	−	1.40052i	0.884341	−	0.466841i
$10$	2.43246	+	2.02068i	0.769211	+	0.638995i
$11$	−2.63380			−0.794119			−0.397060	−	0.917793i	$-0.629969\pi$
$11$	−2.63380			−0.794119			−0.397060	+	0.917793i	$0.629969\pi$
$12$	−3.22192	+	1.27249i	−0.930089	+	0.367335i
$13$	−3.49376	−	3.49376i	−0.968995	−	0.968995i	0.0305386	−	0.999534i	$-0.490278\pi$
$13$	−3.49376	−	3.49376i	−0.968995	−	0.968995i	−0.999534	+	0.0305386i	$0.990278\pi$
$14$	−0.544885	−	0.476703i	−0.145627	−	0.127404i
$15$	−3.36685	−	1.91423i	−0.869318	−	0.494253i
$16$	3.85872	−	1.05369i	0.964681	−	0.263423i
$17$	−3.61339	+	3.61339i	−0.876376	+	0.876376i	−0.993158	−	0.116782i	$-0.962742\pi$
$17$	−3.61339	+	3.61339i	−0.876376	+	0.876376i	0.116782	+	0.993158i	$0.462742\pi$
$18$	3.61172	−	2.22609i	0.851290	−	0.524696i
$19$	0.672266			0.154228			0.0771142	−	0.997022i	$-0.475429\pi$
$19$	0.672266			0.154228			0.0771142	+	0.997022i	$0.475429\pi$
$20$	3.62268	+	2.62225i	0.810056	+	0.586353i
$21$	0.759360	+	0.457809i	0.165706	+	0.0999022i
$22$	−3.71648	+	0.248041i	−0.792357	+	0.0528826i
$23$	−4.31851	−	4.31851i	−0.900472	−	0.900472i	0.0950052	−	0.995477i	$-0.469713\pi$
$23$	−4.31851	−	4.31851i	−0.900472	−	0.900472i	−0.995477	+	0.0950052i	$0.969713\pi$
$24$	−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
$27$	−3.87698	+	3.45963i	−0.746125	+	0.665806i
$28$	−0.813767	−	0.621348i	−0.153787	−	0.117424i
$29$		−	4.76080i		−	0.884058i	−0.897001	−	0.442029i	$-0.854259\pi$
$29$		−	4.76080i		−	0.884058i	0.897001	−	0.442029i	$-0.145741\pi$
$30$	−4.93116	−	2.38405i	−0.900302	−	0.435266i
$31$	3.73793			0.671352			0.335676	−	0.941978i	$-0.391035\pi$
$31$	3.73793			0.671352			0.335676	+	0.941978i	$0.391035\pi$
$32$	5.34571	−	1.85024i	0.944997	−	0.327079i
$33$	4.42800	−	1.09703i	0.770816	−	0.190968i
$34$	−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	$-0.643628\pi$
$37$	2.82150	−	2.82150i	0.463851	−	0.463851i	0.899915	+	0.436064i	$0.143628\pi$
$38$	0.948617	−	0.0633116i	0.153886	−	0.0102705i
$39$	7.32901	+	4.41857i	1.17358	+	0.707538i
$40$	5.35882	+	3.35902i	0.847305	+	0.531107i
$41$			4.10027i			0.640355i	0.947358	+	0.320177i	$0.103743\pi$
$41$			4.10027i			0.640355i	−0.947358	+	0.320177i	$0.896257\pi$
$42$	1.11463	+	0.574489i	0.171991	+	0.0886456i
$43$	7.57996	+	7.57996i	1.15593	+	1.15593i	0.985342	+	0.170591i	$0.0545678\pi$
$43$	7.57996	+	7.57996i	1.15593	+	1.15593i	0.170591	+	0.985342i	$0.445432\pi$
$44$	−5.22087	+	0.700010i	−0.787076	+	0.105530i
$45$	6.45775	+	1.81590i	0.962664	+	0.270698i
$46$	−6.50044	−	5.68704i	−0.958438	−	0.838508i
$47$	−0.987537	+	0.987537i	−0.144047	+	0.144047i	−0.775453	−	0.631406i	$-0.782478\pi$
$47$	−0.987537	+	0.987537i	−0.144047	+	0.144047i	0.631406	+	0.775453i	$0.282478\pi$
$48$	−6.04849	+	3.37872i	−0.873025	+	0.487676i
$49$		−	6.73793i		−	0.962561i
$50$	0.830850	+	7.02209i	0.117500	+	0.993073i
$51$	4.56987	−	7.57996i	0.639910	−	1.06141i
$52$	−7.85412	−	5.99698i	−1.08917	−	0.831631i
$53$	−0.646149	+	0.646149i	−0.0887554	+	0.0887554i	−0.750091	−	0.661335i	$-0.769990\pi$
$53$	−0.646149	+	0.646149i	−0.0887554	+	0.0887554i	0.661335	+	0.750091i	$0.269990\pi$
$54$	−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
$57$	−1.13023	+	0.280012i	−0.149702	+	0.0370884i
$58$	−0.448355	−	6.71784i	−0.0588719	−	0.882096i
$59$			4.92247i			0.640851i	0.947274	+	0.320425i	$0.103826\pi$
$59$			4.92247i			0.640851i	−0.947274	+	0.320425i	$0.896174\pi$
$60$	−7.18275	−	2.89967i	−0.927289	−	0.374346i
$61$			6.07190i			0.777428i	0.921359	+	0.388714i	$0.127081\pi$
$61$			6.07190i			0.777428i	−0.921359	+	0.388714i	$0.872919\pi$
$62$	5.27449	−	0.352025i	0.669861	−	0.0447072i
$63$	−1.46734	−	0.453392i	−0.184868	−	0.0571220i
$64$	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	$-0.740399\pi$
$67$	0.349085	−	0.349085i	0.0426476	−	0.0426476i	0.728109	+	0.685461i	$0.240399\pi$
$68$	−6.20232	+	8.12305i	−0.752141	+	0.985064i
$69$	9.05912	+	5.46164i	1.09059	+	0.657504i
$70$	−0.149059	−	1.61199i	−0.0178160	−	0.192669i
$71$			8.63702i			1.02503i	0.858680	+	0.512513i	$0.171285\pi$
$71$			8.63702i			1.02503i	−0.858680	+	0.512513i	$0.828715\pi$
$72$	6.56772	−	5.37262i	0.774013	−	0.633170i
$73$	−11.3261	+	11.3261i	−1.32562	+	1.32562i	−0.416465	+	0.909152i	$0.636731\pi$
$73$	−11.3261	+	11.3261i	−1.32562	+	1.32562i	−0.909152	+	0.416465i	$0.863269\pi$
$74$	3.71562	−	4.24706i	0.431932	−	0.493711i
$75$	−2.50949	−	8.28869i	−0.289771	−	0.957096i
$76$	1.33261	−	0.178675i	0.152860	−	0.0204954i
$77$	0.953406	+	0.953406i	0.108651	+	0.108651i
$78$	10.7579	+	5.54472i	1.21809	+	0.627816i
$79$		−	4.07707i		−	0.458706i	−0.973343	−	0.229353i	$-0.926339\pi$
$79$		−	4.07707i		−	0.458706i	0.973343	−	0.229353i	$-0.0736610\pi$
$80$	7.87804	+	4.23515i	0.880792	+	0.473504i
$81$	5.07707	−	7.43124i	0.564119	−	0.825694i
$82$	0.386149	+	5.78579i	0.0426430	+	0.638933i
$83$	8.53893	−	8.53893i	0.937270	−	0.937270i	−0.0608758	−	0.998145i	$-0.519389\pi$
$83$	8.53893	−	8.53893i	0.937270	−	0.937270i	0.998145	+	0.0608758i	$0.0193894\pi$
$84$	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
$87$	1.98296	+	8.00397i	0.212596	+	0.858115i
$88$	−7.30111	+	1.47945i	−0.778301	+	0.157710i
$89$	6.58584			0.698097			0.349049	−	0.937105i	$-0.386505\pi$
$89$	6.58584			0.698097			0.349049	+	0.937105i	$0.386505\pi$
$90$	9.28338	+	1.95420i	0.978554	+	0.205990i
$91$			2.52941i			0.265154i
$92$	−9.70819	−	7.41264i	−1.01215	−	0.772822i
$93$	−6.28429	+	1.55692i	−0.651651	+	0.161445i
$94$	−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	0.672760	−	0.739860i	$-0.265108\pi$
$97$	−0.660859	−	0.660859i	−0.0671001	−	0.0671001i	−0.739860	+	0.672760i	$0.765108\pi$
$98$	−0.634554	−	9.50772i	−0.0640996	−	0.960424i
$99$	−6.98752	+	3.68869i	−0.702272	+	0.370728i
$100$	1.83371	+	9.83044i	0.183371	+	0.983044i
$101$	−3.46850			−0.345129			−0.172564	−	0.984998i	$-0.555205\pi$
$101$	−3.46850			−0.345129			−0.172564	+	0.984998i	$0.555205\pi$
$102$	5.73457	−	11.1263i	0.567807	−	1.10166i
$103$	8.68806	−	8.68806i	0.856060	−	0.856060i	−0.134811	−	0.990871i	$-0.543043\pi$
$103$	8.68806	−	8.68806i	0.856060	−	0.856060i	0.990871	+	0.134811i	$0.0430428\pi$
$104$	−11.6475	−	7.72251i	−1.14213	−	0.757254i
$105$	0.525833	+	1.91170i	0.0513160	+	0.186563i
$106$	−0.850913	+	0.972617i	−0.0826480	+	0.0944689i
$107$	3.10967	+	3.10967i	0.300623	+	0.300623i	0.841258	−	0.540634i	$-0.181816\pi$
$107$	3.10967	+	3.10967i	0.300623	+	0.300623i	−0.540634	+	0.841258i	$0.681816\pi$
$108$	−6.76569	+	7.88831i	−0.651029	+	0.759053i
$109$	−4.14320			−0.396846			−0.198423	−	0.980116i	$-0.563582\pi$
$109$	−4.14320			−0.396846			−0.198423	+	0.980116i	$0.563582\pi$
$110$	−6.40660	−	5.32206i	−0.610845	−	0.507438i
$111$	−3.56836	+	5.91877i	−0.338693	+	0.561785i
$112$	−1.77824	−	1.01539i	−0.168028	−	0.0959455i
$113$	−4.38269	−	4.38269i	−0.412289	−	0.412289i	0.470247	−	0.882535i	$-0.344165\pi$
$113$	−4.38269	−	4.38269i	−0.412289	−	0.412289i	−0.882535	+	0.470247i	$0.844165\pi$
$114$	−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
$117$	−14.1621	−	4.37594i	−1.30929	−	0.404555i
$118$	0.463580	+	6.94597i	0.0426760	+	0.639428i
$119$	2.61602			0.239810
$120$	−10.4085	−	3.41521i	−0.950160	−	0.311764i
$121$	−4.06312			−0.369374
$122$	0.571830	+	8.56791i	0.0517711	+	0.775702i
$123$	−1.70784	−	6.89347i	−0.153991	−	0.621563i
$124$	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	0.993258	−	0.115927i	$-0.0369839\pi$
$127$	9.88701	+	9.88701i	0.877331	+	0.877331i	−0.115927	+	0.993258i	$0.536984\pi$
$128$	10.1048	−	5.08843i	0.893150	−	0.449758i
$129$	−15.9008	−	9.58641i	−1.39999	−	0.844036i
$130$	−1.43866	−	15.5582i	−0.126178	−	1.36454i
$131$	−8.79462			−0.768389			−0.384195	−	0.923252i	$-0.625521\pi$
$131$	−8.79462			−0.768389			−0.384195	+	0.923252i	$0.625521\pi$
$132$	8.48588	−	3.35147i	0.738601	−	0.291708i
$133$	−0.243353	−	0.243353i	−0.0211014	−	0.0211014i
$134$	0.459710	−	0.525461i	0.0397129	−	0.0453929i
$135$	−11.6133	−	0.363150i	−0.999511	−	0.0312550i
$136$	−7.98693	+	12.0463i	−0.684874	+	1.03297i
$137$	1.48819	−	1.48819i	0.127145	−	0.127145i	−0.640671	−	0.767816i	$-0.721344\pi$
$137$	1.48819	−	1.48819i	0.127145	−	0.127145i	0.767816	+	0.640671i	$0.221344\pi$
$138$	13.2975	+	6.85362i	1.13195	+	0.583419i
$139$	−13.3028			−1.12833			−0.564164	−	0.825663i	$-0.690801\pi$
$139$	−13.3028			−1.12833			−0.564164	+	0.825663i	$0.690801\pi$
$140$	−0.362145	−	2.26060i	−0.0306068	−	0.191055i
$141$	1.24894	−	2.07160i	0.105180	−	0.174460i
$142$	0.813404	+	12.1875i	0.0682593	+	1.02275i
$143$	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
$147$	2.80648	+	11.3280i	0.231474	+	0.934314i
$148$	4.84305	−	6.34284i	0.398096	−	0.521378i
$149$		−	5.22462i		−	0.428018i	−0.976832	−	0.214009i	$-0.931348\pi$
$149$		−	5.22462i		−	0.428018i	0.976832	−	0.214009i	$-0.0686522\pi$
$150$	−4.32168	−	11.4596i	−0.352864	−	0.935675i
$151$	−11.8511			−0.964429			−0.482214	−	0.876053i	$-0.660167\pi$
$151$	−11.8511			−0.964429			−0.482214	+	0.876053i	$0.660167\pi$
$152$	1.86358	−	0.377623i	0.151156	−	0.0306293i
$153$	−4.52577	+	14.6470i	−0.365887	+	1.18414i
$154$	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	0.120836	−	0.992673i	$-0.461443\pi$
$157$	13.9522	−	13.9522i	1.11351	−	1.11351i	0.992673	−	0.120836i	$-0.0385574\pi$
$158$	−0.383964	−	5.75305i	−0.0305465	−	0.457688i
$159$	0.817188	−	1.35546i	0.0648072	−	0.107495i
$160$	11.5154	+	5.23418i	0.910368	+	0.413799i
$161$			3.12651i			0.246403i
$162$	6.46427	−	10.9642i	0.507881	−	0.861427i
$163$	6.66434	+	6.66434i	0.521992	+	0.521992i	0.918172	−	0.396181i	$-0.129665\pi$
$163$	6.66434	+	6.66434i	0.521992	+	0.521992i	−0.396181	+	0.918172i	$0.629665\pi$
$164$	1.08977	+	8.12781i	0.0850967	+	0.634675i
$165$	8.86761	+	5.04170i	0.690342	+	0.392496i
$166$	11.2449	−	12.8532i	0.872774	−	0.997604i
$167$	15.6456	−	15.6456i	1.21069	−	1.21069i	0.239890	−	0.970800i	$-0.422889\pi$
$167$	15.6456	−	15.6456i	1.21069	−	1.21069i	0.970800	−	0.239890i	$-0.0771113\pi$
$168$	2.36217	+	0.842542i	0.182246	+	0.0650035i
$169$			11.4127i			0.877903i
$170$	−16.0909	+	1.48792i	−1.23412	+	0.114118i
$171$	1.78354	−	0.941524i	0.136390	−	0.0720001i
$172$	17.0401	+	13.0109i	1.29929	+	0.992069i
$173$	−6.40332	+	6.40332i	−0.486836	+	0.486836i	−0.907306	−	0.420471i	$-0.861865\pi$
$173$	−6.40332	+	6.40332i	−0.486836	+	0.486836i	0.420471	+	0.907306i	$0.361865\pi$
$174$	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
$177$	−2.05030	−	8.27577i	−0.154110	−	0.622045i
$178$	9.29311	−	0.620231i	0.696548	−	0.0464882i
$179$			0.582525i			0.0435399i	0.999763	+	0.0217700i	$0.00693014\pi$
$179$			0.582525i			0.0435399i	−0.999763	+	0.0217700i	$0.993070\pi$
$180$	13.2836	+	1.88324i	0.990099	+	0.140369i
$181$			3.71429i			0.276081i	0.990427	+	0.138040i	$0.0440804\pi$
$181$			3.71429i			0.276081i	−0.990427	+	0.138040i	$0.955920\pi$
$182$	0.238211	+	3.56918i	0.0176573	+	0.264565i
$183$	−2.52906	−	10.2082i	−0.186954	−	0.754614i
$184$	−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
$188$	−1.69509	+	2.22002i	−0.123627	+	0.161912i
$189$	2.65577	+	0.151077i	0.193179	+	0.0109892i
$190$	1.63526	+	1.35843i	0.118634	+	0.0985511i
$191$		−	22.4496i		−	1.62440i	−0.583380	−	0.812199i	$-0.698270\pi$
$191$		−	22.4496i		−	1.62440i	0.583380	−	0.812199i	$-0.301730\pi$
$192$	−11.0917	+	8.30507i	−0.800474	+	0.599367i
$193$	8.01395	−	8.01395i	0.576857	−	0.576857i	−0.357179	−	0.934036i	$-0.616261\pi$
$193$	8.01395	−	8.01395i	0.576857	−	0.576857i	0.934036	+	0.357179i	$0.116261\pi$
$194$	−0.994759	−	0.870284i	−0.0714195	−	0.0624828i
$195$	5.07511	+	18.4509i	0.363436	+	1.32129i
$196$	−1.79081	−	13.3563i	−0.127915	−	0.954024i
$197$	1.49806	+	1.49806i	0.106733	+	0.106733i	0.758456	−	0.651724i	$-0.225954\pi$
$197$	1.49806	+	1.49806i	0.106733	+	0.106733i	−0.651724	+	0.758456i	$0.725954\pi$
$198$	−9.51253	+	5.86308i	−0.676026	+	0.416671i
$199$			12.6160i			0.894328i	0.894452	+	0.447164i	$0.147566\pi$
$199$			12.6160i			0.894328i	−0.894452	+	0.447164i	$0.852434\pi$
$200$	3.51329	+	13.6988i	0.248427	+	0.968651i
$201$	−0.441490	+	0.732291i	−0.0311403	+	0.0516519i
$202$	−4.89431	+	0.326651i	−0.344363	+	0.0229831i
$203$	−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
$207$	−17.5053	−	5.40893i	−1.21670	−	0.375947i
$208$	−17.1628	−	9.80011i	−1.19003	−	0.679515i
$209$	−1.77061			−0.122476
$210$	0.922026	+	2.64803i	0.0636258	+	0.182731i
$211$			14.0010i			0.963865i	0.876208	+	0.481933i	$0.160065\pi$
$211$			14.0010i			0.963865i	−0.876208	+	0.481933i	$0.839935\pi$
$212$	−1.10910	+	1.45257i	−0.0761736	+	0.0997630i
$213$	−3.59748	−	14.5208i	−0.246496	−	0.994946i
$214$	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
$218$	−5.84636	+	0.390192i	−0.395965	+	0.0264271i
$219$	14.3241	−	23.7592i	0.967935	−	1.60550i
$220$	−9.54140	−	6.90647i	−0.643281	−	0.465634i
$221$	25.2486			1.69841
$222$	−4.47781	+	8.68788i	−0.300531	+	0.583092i
$223$	−2.56530	+	2.56530i	−0.171785	+	0.171785i	−0.787763	−	0.615978i	$-0.788761\pi$
$223$	−2.56530	+	2.56530i	−0.171785	+	0.171785i	0.615978	+	0.787763i	$0.288761\pi$
$224$	−2.60486	−	1.26532i	−0.174044	−	0.0845431i
$225$	7.67141	+	12.8899i	0.511428	+	0.859326i
$226$	−6.59704	−	5.77155i	−0.438829	−	0.383918i
$227$	−13.3645	−	13.3645i	−0.887032	−	0.887032i	0.107205	−	0.994237i	$-0.465810\pi$
$227$	−13.3645	−	13.3645i	−0.887032	−	0.887032i	−0.994237	+	0.107205i	$0.965810\pi$
$228$	−2.16599	+	0.855448i	−0.143446	+	0.0566534i
$229$	15.7606			1.04149			0.520746	−	0.853712i	$-0.325654\pi$
$229$	15.7606			1.04149			0.520746	+	0.853712i	$0.325654\pi$
$230$	−1.77827	−	19.2309i	−0.117256	−	1.26805i
$231$	−2.00000	−	1.20578i	−0.131590	−	0.0793343i
$232$	−2.67422	−	13.1974i	−0.175571	−	0.866449i
$233$	13.0197	+	13.0197i	0.852949	+	0.852949i	0.990495	−	0.137546i	$-0.0439215\pi$
$233$	13.0197	+	13.0197i	0.852949	+	0.852949i	−0.137546	+	0.990495i	$0.543921\pi$
$234$	−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
$237$	1.69818	+	6.85446i	0.110308	+	0.445245i
$238$	3.69139	−	0.246367i	0.239278	−	0.0159696i
$239$	−24.8336			−1.60635			−0.803177	−	0.595740i	$-0.796859\pi$
$239$	−24.8336			−1.60635			−0.803177	+	0.595740i	$0.796859\pi$
$240$	−15.0088	−	3.83888i	−0.968812	−	0.247798i
$241$	17.2991			1.11433			0.557165	−	0.830402i	$-0.311889\pi$
$241$	17.2991			1.11433			0.557165	+	0.830402i	$0.311889\pi$
$242$	−5.73336	+	0.382650i	−0.368555	+	0.0245977i
$243$	−5.44043	+	14.6083i	−0.349004	+	0.937121i
$244$	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
$248$	10.3619	−	2.09966i	0.657979	−	0.133328i
$249$	−10.7992	+	17.9125i	−0.684373	+	1.13516i
$250$	−9.46861	+	12.6628i	−0.598847	+	0.800863i
$251$	−1.05032			−0.0662958			−0.0331479	−	0.999450i	$-0.510553\pi$
$251$	−1.05032			−0.0662958			−0.0331479	+	0.999450i	$0.510553\pi$
$252$	−3.02916	−	0.508751i	−0.190819	−	0.0320483i
$253$	11.3741	+	11.3741i	0.715082	+	0.715082i
$254$	14.8824	+	13.0202i	0.933807	+	0.816959i
$255$	19.0826	−	5.24888i	1.19500	−	0.328698i
$256$	13.7795	−	8.13180i	0.861217	−	0.508237i
$257$	−2.20315	+	2.20315i	−0.137429	+	0.137429i	−0.772474	−	0.635046i	$-0.780981\pi$
$257$	−2.20315	+	2.20315i	−0.137429	+	0.137429i	0.635046	+	0.772474i	$0.280981\pi$
$258$	−23.3400	−	12.0297i	−1.45309	−	0.748934i
$259$	−2.04270			−0.126927
$260$	−3.49527	−	21.8183i	−0.216767	−	1.35311i
$261$	−6.66761	−	12.6305i	−0.412715	−	0.781809i
$262$	−12.4099	+	0.828245i	−0.766683	+	0.0511692i
$263$	−7.49936	−	7.49936i	−0.462430	−	0.462430i	0.437021	−	0.899451i	$-0.356034\pi$
$263$	−7.49936	−	7.49936i	−0.462430	−	0.462430i	−0.899451	+	0.437021i	$0.856034\pi$
$264$	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
$267$	−11.0723	+	2.74313i	−0.677611	+	0.167877i
$268$	0.599199	−	0.784759i	0.0366019	−	0.0479368i
$269$		−	21.1993i		−	1.29254i	−0.763108	−	0.646271i	$-0.776327\pi$
$269$		−	21.1993i		−	1.29254i	0.763108	−	0.646271i	$-0.223673\pi$
$270$	−16.4214	+	0.581264i	−0.999374	+	0.0353746i
$271$	−14.6748			−0.891431			−0.445716	−	0.895175i	$-0.647051\pi$
$271$	−14.6748			−0.891431			−0.445716	+	0.895175i	$0.647051\pi$
$272$	−10.1357	+	17.7505i	−0.614565	+	1.07628i
$273$	−1.05355	−	4.25250i	−0.0637636	−	0.257373i
$274$	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	$-0.871912\pi$
$277$	−8.79593	+	8.79593i	−0.528496	+	0.528496i	0.391628	+	0.920124i	$0.371912\pi$
$278$	−18.7712	+	1.25281i	−1.12582	+	0.0751384i
$279$	9.91681	−	5.23506i	0.593704	−	0.313415i
$280$	−0.723909	−	3.15577i	−0.0432618	−	0.188593i
$281$		−	0.490821i		−	0.0292799i	−0.999893	−	0.0146399i	$-0.995340\pi$
$281$		−	0.490821i		−	0.0292799i	0.999893	−	0.0146399i	$-0.00466021\pi$
$282$	1.56726	−	3.04080i	0.0933287	−	0.181077i
$283$	−9.43710	−	9.43710i	−0.560978	−	0.560978i	0.368608	−	0.929585i	$-0.379835\pi$
$283$	−9.43710	−	9.43710i	−0.560978	−	0.560978i	−0.929585	+	0.368608i	$0.879835\pi$
$284$	2.29555	+	17.1208i	0.136216	+	1.01593i
$285$	−2.26342	−	1.28687i	−0.134073	−	0.0762278i
$286$	13.8511	+	12.1179i	0.819033	+	0.716547i
$287$	1.48425	−	1.48425i	0.0876127	−	0.0876127i
$288$	11.5910	−	12.3955i	0.683006	−	0.730413i
$289$		−	9.11317i		−	0.536069i
$290$	9.62005	−	11.5804i	0.564909	−	0.680027i
$291$	1.38631	+	0.835791i	0.0812671	+	0.0489950i
$292$	−19.4410	+	25.4615i	−1.13770	+	1.49002i
$293$	−4.01316	+	4.01316i	−0.234451	+	0.234451i	−0.814548	−	0.580096i	$-0.803015\pi$
$293$	−4.01316	+	4.01316i	−0.234451	+	0.234451i	0.580096	+	0.814548i	$0.303015\pi$
$294$	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
$297$	10.2112	−	9.11195i	0.592512	−	0.528729i
$298$	−0.492036	−	7.37233i	−0.0285029	−	0.427068i
$299$			30.1757i			1.74510i
$300$	−7.17744	−	15.7634i	−0.414389	−	0.910100i
$301$		−	5.48773i		−	0.316307i
$302$	−16.7228	+	1.11609i	−0.962288	+	0.0642240i
$303$	5.83132	−	1.44470i	0.335001	−	0.0829957i
$304$	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	$-0.854763\pi$
$307$	−8.00887	+	8.00887i	−0.457091	+	0.457091i	0.440609	+	0.897699i	$0.354763\pi$
$308$	2.14330	+	1.63650i	0.122126	+	0.0932485i
$309$	−10.9878	+	18.2253i	−0.625076	+	1.03680i
$310$	9.09235	+	7.55315i	0.516411	+	0.428990i
$311$		−	12.8874i		−	0.730778i	−0.930855	−	0.365389i	$-0.880936\pi$
$311$		−	12.8874i		−	0.730778i	0.930855	−	0.365389i	$-0.119064\pi$
$312$	22.7987	+	8.13185i	1.29072	+	0.460375i
$313$	12.2991	−	12.2991i	0.695184	−	0.695184i	−0.268184	−	0.963368i	$-0.586424\pi$
$313$	12.2991	−	12.2991i	0.695184	−	0.695184i	0.963368	+	0.268184i	$0.0864235\pi$
$314$	18.3736	−	21.0016i	1.03688	−	1.18519i
$315$	−1.68030	−	2.99497i	−0.0946742	−	0.168747i
$316$	−1.08360	−	8.08182i	−0.0609574	−	0.454638i
$317$	9.24176	+	9.24176i	0.519069	+	0.519069i	0.917290	−	0.398221i	$-0.130372\pi$
$317$	9.24176	+	9.24176i	0.519069	+	0.519069i	−0.398221	+	0.917290i	$0.630372\pi$
$318$	1.02546	−	1.98961i	0.0575050	−	0.111572i
$319$			12.5390i			0.702048i
$320$	16.7420	+	6.30135i	0.935904	+	0.352256i
$321$	−6.52329	−	3.93281i	−0.364094	−	0.219508i
$322$	0.294443	+	4.41174i	0.0164087	+	0.245856i
$323$	−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
$327$	6.96564	−	1.72572i	0.385201	−	0.0954326i
$328$	2.30319	+	11.3663i	0.127173	+	0.627600i
$329$	0.714956			0.0394168
$330$	12.9877	+	6.27910i	0.714947	+	0.345653i
$331$		−	22.2355i		−	1.22218i	−0.791563	−	0.611088i	$-0.790732\pi$
$331$		−	22.2355i		−	1.22218i	0.791563	−	0.611088i	$-0.209268\pi$
$332$	14.6569	−	19.1959i	0.804403	−	1.05351i
$333$	3.53392	−	11.4371i	0.193658	−	0.626747i
$334$	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	0.418615	−	0.908164i	$-0.362516\pi$
$337$	−8.98693	−	8.98693i	−0.489549	−	0.489549i	−0.908164	+	0.418615i	$0.862516\pi$
$338$	1.07481	+	16.1042i	0.0584620	+	0.875954i
$339$	9.19375	+	5.54280i	0.499336	+	0.301044i
$340$	−22.5654	+	3.61495i	−1.22378	+	0.196048i
$341$	−9.84494			−0.533133
$342$	2.42803	−	1.49653i	0.131293	−	0.0809229i
$343$	−4.97298	+	4.97298i	−0.268516	+	0.268516i
$344$	25.2701	+	16.7545i	1.36247	+	0.903343i
$345$	6.27315	+	22.8064i	0.337735	+	1.22786i
$346$	−8.43252	+	9.63861i	−0.453335	+	0.518175i
$347$	9.25494	+	9.25494i	0.496831	+	0.496831i	0.910450	−	0.413619i	$-0.135735\pi$
$347$	9.25494	+	9.25494i	0.496831	+	0.496831i	−0.413619	+	0.910450i	$0.635735\pi$
$348$	6.05805	+	15.3389i	0.324745	+	0.822253i
$349$	−17.5919			−0.941671			−0.470835	−	0.882221i	$-0.656047\pi$
$349$	−17.5919			−0.941671			−0.470835	+	0.882221i	$0.656047\pi$
$350$	2.24116	−	2.84268i	0.119795	−	0.151948i
$351$	25.6324	+	1.45813i	1.36815	+	0.0778292i
$352$	−14.0795	+	4.87314i	−0.750440	+	0.259739i
$353$	−12.9654	−	12.9654i	−0.690077	−	0.690077i	0.272172	−	0.962249i	$-0.412258\pi$
$353$	−12.9654	−	12.9654i	−0.690077	−	0.690077i	−0.962249	+	0.272172i	$0.912258\pi$
$354$	−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
$357$	−4.39811	+	1.08962i	−0.232773	+	0.0576689i
$358$	0.0548601	+	0.821985i	0.00289945	+	0.0434433i
$359$	−16.5244			−0.872125			−0.436063	−	0.899916i	$-0.643627\pi$
$359$	−16.5244			−0.872125			−0.436063	+	0.899916i	$0.643627\pi$
$360$	18.9215	+	1.40639i	0.997249	+	0.0741235i
$361$	−18.5481			−0.976214
$362$	0.349798	+	5.24113i	0.0183850	+	0.275468i
$363$	6.83101	−	1.69237i	0.358535	−	0.0888262i
$364$	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	−0.941581	−	0.336786i	$-0.890660\pi$
$367$	−24.4900	−	24.4900i	−1.27837	−	1.27837i	−0.336786	−	0.941581i	$-0.609340\pi$
$368$	−21.2143	−	12.1136i	−1.10587	−	0.631463i
$369$	5.74253	+	10.8781i	0.298944	+	0.566292i
$370$	12.5645	−	1.16183i	0.653198	−	0.0604007i
$371$	0.467798			0.0242869
$372$	−12.0433	+	4.75646i	−0.624417	+	0.246611i
$373$	−0.406084	−	0.406084i	−0.0210262	−	0.0210262i	0.696516	−	0.717542i	$-0.254733\pi$
$373$	−0.406084	−	0.406084i	−0.0210262	−	0.0210262i	−0.717542	+	0.696516i	$0.754733\pi$
$374$	12.5328	−	14.3254i	0.648057	−	0.740747i
$375$	8.69830	−	17.3014i	0.449178	−	0.893442i
$376$	−2.18282	+	3.29226i	−0.112571	+	0.169785i
$377$	−16.6331	+	16.6331i	−0.856648	+	0.856648i
$378$	3.76172	−	0.0369302i	0.193482	−	0.00189948i
$379$	−5.73108			−0.294386			−0.147193	−	0.989108i	$-0.547024\pi$
$379$	−5.73108			−0.294386			−0.147193	+	0.989108i	$0.547024\pi$
$380$	2.43540	+	1.76285i	0.124934	+	0.0904322i
$381$	−20.7404	−	12.5041i	−1.06256	−	0.640607i
$382$	−2.11423	−	31.6781i	−0.108173	−	1.62079i
$383$	17.2603	+	17.2603i	0.881958	+	0.881958i	0.993734	−	0.111775i	$-0.0356537\pi$
$383$	17.2603	+	17.2603i	0.881958	+	0.881958i	−0.111775	+	0.993734i	$0.535654\pi$
$384$	−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
$387$	30.7257	+	9.49390i	1.56188	+	0.482602i
$388$	−1.48564	−	1.13435i	−0.0754219	−	0.0575880i
$389$			27.9300i			1.41611i	0.706159	+	0.708053i	$0.250426\pi$
$389$			27.9300i			1.41611i	−0.706159	+	0.708053i	$0.749574\pi$
$390$	8.89899	+	25.5576i	0.450618	+	1.29416i
$391$	31.2089			1.57830
$392$	−3.78481	−	18.6781i	−0.191162	−	0.943388i
$393$	14.7857	−	3.66313i	0.745841	−	0.184780i
$394$	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	$-0.785798\pi$
$397$	−3.16232	+	3.16232i	−0.158712	+	0.158712i	0.623284	+	0.781996i	$0.285798\pi$
$398$	1.18813	+	17.8022i	0.0595558	+	0.892342i
$399$	0.510492	+	0.307770i	0.0255566	+	0.0154077i
$400$	6.24762	+	18.9991i	0.312381	+	0.949957i
$401$		−	11.2530i		−	0.561950i	−0.959715	−	0.280975i	$-0.909342\pi$
$401$		−	11.2530i		−	0.561950i	0.959715	−	0.280975i	$-0.0906578\pi$
$402$	−0.554010	+	1.07490i	−0.0276315	+	0.0536109i
$403$	−13.0594	−	13.0594i	−0.650536	−	0.650536i
$404$	−6.87548	+	0.921858i	−0.342068	+	0.0458641i
$405$	19.6758	−	4.22661i	0.977697	−	0.210022i
$406$	−2.26949	+	2.59409i	−0.112633	+	0.128742i
$407$	−7.43124	+	7.43124i	−0.368353	+	0.368353i
$408$	8.41028	−	23.5793i	0.416371	−	1.16735i
$409$		−	5.05965i		−	0.250183i	−0.992145	−	0.125092i	$-0.960077\pi$
$409$		−	5.05965i		−	0.250183i	0.992145	−	0.125092i	$-0.0399225\pi$
$410$	−8.28533	+	9.97374i	−0.409184	+	0.492568i
$411$	−1.88212	+	3.12185i	−0.0928384	+	0.153989i
$412$	14.9129	−	19.5311i	0.734706	−	0.962229i
$413$	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
$417$	22.3649	−	5.54086i	1.09522	−	0.271337i
$418$	−2.49846	+	0.166750i	−0.122204	+	0.00815600i
$419$		−	25.1822i		−	1.23023i	−0.788436	−	0.615116i	$-0.789109\pi$
$419$		−	25.1822i		−	1.23023i	0.788436	−	0.615116i	$-0.210891\pi$
$420$	1.55043	+	3.64973i	0.0756532	+	0.178089i
$421$			31.5091i			1.53566i	0.640654	+	0.767830i	$0.278664\pi$
$421$			31.5091i			1.53566i	−0.640654	+	0.767830i	$0.721336\pi$
$422$	1.31856	+	19.7564i	0.0641865	+	0.961726i
$423$	−1.23689	+	4.00303i	−0.0601397	+	0.194634i
$424$	−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
$428$	6.99067	+	5.33769i	0.337907	+	0.258007i
$429$	−19.3031	−	11.6376i	−0.931963	−	0.561870i
$430$	3.12126	+	33.7546i	0.150521	+	1.62779i
$431$			13.6082i			0.655482i	0.944768	+	0.327741i	$0.106287\pi$
$431$			13.6082i			0.655482i	−0.944768	+	0.327741i	$0.893713\pi$
$432$	−11.3148	+	17.4349i	−0.544384	+	0.838836i
$433$	2.81500	−	2.81500i	0.135280	−	0.135280i	−0.636224	−	0.771504i	$-0.719505\pi$
$433$	2.81500	−	2.81500i	0.135280	−	0.135280i	0.771504	+	0.636224i	$0.219505\pi$
$434$	−2.03674	−	1.78188i	−0.0977666	−	0.0855330i
$435$	−9.11329	+	16.0289i	−0.436949	+	0.768528i
$436$	−8.21290	+	1.10118i	−0.393327	+	0.0527369i
$437$	−2.90319	−	2.90319i	−0.138878	−	0.138878i
$438$	17.9749	−	34.8750i	0.858872	−	1.66639i
$439$		−	5.56599i		−	0.265650i	−0.991139	−	0.132825i	$-0.957595\pi$
$439$		−	5.56599i		−	0.265650i	0.991139	−	0.132825i	$-0.0424049\pi$
$440$	−14.1140	−	8.84697i	−0.672861	−	0.421763i
$441$	−9.43663	−	17.8759i	−0.449363	−	0.851232i
$442$	35.6277	−	2.37783i	1.69464	−	0.113102i
$443$	−3.53450	+	3.53450i	−0.167929	+	0.167929i	−0.786069	−	0.618139i	$-0.787887\pi$
$443$	−3.53450	+	3.53450i	−0.167929	+	0.167929i	0.618139	+	0.786069i	$0.287887\pi$
$444$	−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
$447$	2.17616	+	8.78376i	0.102929	+	0.415458i
$448$	−3.79481	−	1.54015i	−0.179288	−	0.0727653i
$449$	21.1895			0.999995			0.499998	−	0.866027i	$-0.333334\pi$
$449$	21.1895			0.999995			0.499998	+	0.866027i	$0.333334\pi$
$450$	12.0389	+	17.4661i	0.567517	+	0.823361i
$451$		−	10.7993i		−	0.508518i
$452$	−9.85246	−	7.52280i	−0.463421	−	0.353843i
$453$	19.9243	−	4.93621i	0.936127	−	0.231923i
$454$	−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	0.981423	−	0.191857i	$-0.0614509\pi$
$457$	16.8790	+	16.8790i	0.789566	+	0.789566i	−0.191857	+	0.981423i	$0.561451\pi$
$458$	22.2394	−	1.48428i	1.03918	−	0.0693558i
$459$	1.50806	−	26.5100i	0.0703901	−	1.23738i
$460$	−4.32037	−	26.9688i	−0.201438	−	1.25743i
$461$	3.58886			0.167150			0.0835749	−	0.996502i	$-0.473366\pi$
$461$	3.58886			0.167150			0.0835749	+	0.996502i	$0.473366\pi$
$462$	−2.93570	−	1.51309i	−0.136581	−	0.0703952i
$463$	−26.4996	+	26.4996i	−1.23154	+	1.23154i	−0.268168	+	0.963372i	$0.586418\pi$
$463$	−26.4996	+	26.4996i	−1.23154	+	1.23154i	−0.963372	+	0.268168i	$0.913582\pi$
$464$	−5.01641	−	18.3706i	−0.232881	−	0.852834i
$465$	−12.5851	−	7.15527i	−0.583618	−	0.331818i
$466$	19.5979	+	17.1456i	0.907856	+	0.794256i
$467$	−21.1839	−	21.1839i	−0.980274	−	0.980274i	0.0195348	−	0.999809i	$-0.493781\pi$
$467$	−21.1839	−	21.1839i	−0.980274	−	0.980274i	−0.999809	+	0.0195348i	$0.993781\pi$
$468$	−29.2361	−	4.91024i	−1.35144	−	0.226976i
$469$	−0.252730			−0.0116700
$470$	−4.39764	+	0.406647i	−0.202848	+	0.0187572i
$471$	−17.6454	+	29.2682i	−0.813058	+	1.34861i
$472$	2.76504	+	13.6455i	0.127271	+	0.628086i
$473$	−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
$477$	−0.809302	+	2.61920i	−0.0370554	+	0.119925i
$478$	−35.0421	+	2.33874i	−1.60279	+	0.106972i
$479$	2.58847			0.118270			0.0591350	−	0.998250i	$-0.481166\pi$
$479$	2.58847			0.118270			0.0591350	+	0.998250i	$0.481166\pi$
$480$	−21.5400	−	4.00347i	−0.983163	−	0.182732i
$481$	−19.7153			−0.898939
$482$	24.4103	−	1.62916i	1.11186	−	0.0742063i
$483$	−1.30225	−	5.25636i	−0.0592545	−	0.239173i
$484$	−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	0.869692	−	0.493595i	$-0.164317\pi$
$487$	8.29975	+	8.29975i	0.376098	+	0.376098i	−0.493595	+	0.869692i	$0.664317\pi$
$488$	3.41069	+	16.8319i	0.154395	+	0.761942i
$489$	−13.9801	−	8.42842i	−0.632201	−	0.381146i
$490$	13.6152	−	16.3897i	0.615072	−	0.740412i
$491$	25.3703			1.14494			0.572472	−	0.819924i	$-0.305985\pi$
$491$	25.3703			1.14494			0.572472	+	0.819924i	$0.305985\pi$
$492$	−5.21753	−	13.2108i	−0.235225	−	0.595587i
$493$	17.2026	+	17.2026i	0.774767	+	0.774767i
$494$	−3.53544	−	3.09305i	−0.159067	−	0.139163i
$495$	−17.0084	−	4.78270i	−0.764470	−	0.214966i
$496$	14.4236	−	3.93862i	0.647640	−	0.176849i
$497$	3.12651	−	3.12651i	0.140243	−	0.140243i
$498$	−13.5516	+	26.2929i	−0.607261	+	1.17821i
$499$	28.6742			1.28363			0.641816	−	0.766859i	$-0.278181\pi$
$499$	28.6742			1.28363			0.641816	+	0.766859i	$0.278181\pi$
$500$	−12.1684	+	18.7598i	−0.544186	+	0.838964i
$501$	−19.7870	+	32.8204i	−0.884018	+	1.46631i
$502$	−1.48208	+	0.0989156i	−0.0661486	+	0.00441482i
$503$	5.46994	+	5.46994i	0.243893	+	0.243893i	0.818458	−	0.574566i	$-0.194829\pi$
$503$	5.46994	+	5.46994i	0.243893	+	0.243893i	−0.574566	+	0.818458i	$0.694829\pi$
$504$	−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
$507$	−4.75362	−	19.1874i	−0.211116	−	0.852140i
$508$	22.2264	+	16.9709i	0.986138	+	0.752961i
$509$		−	21.6722i		−	0.960605i	−0.877103	−	0.480303i	$-0.840527\pi$
$509$		−	21.6722i		−	0.960605i	0.877103	−	0.480303i	$-0.159473\pi$
$510$	26.4327	−	9.20370i	1.17046	−	0.407547i
$511$	8.19983			0.362739
$512$	18.6780	−	12.7723i	0.825460	−	0.564460i
$513$	−2.60636	+	2.32579i	−0.115074	+	0.102686i
$514$	−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
$518$	−2.88240	+	0.192374i	−0.126646	+	0.00845244i
$519$	8.09831	−	13.4325i	0.355476	−	0.589622i
$520$	−6.98685	−	30.4581i	−0.306394	−	1.33567i
$521$			13.0236i			0.570576i	0.958442	+	0.285288i	$0.0920893\pi$
$521$			13.0236i			0.570576i	−0.958442	+	0.285288i	$0.907911\pi$
$522$	−10.5980	−	17.1947i	−0.463861	−	0.752590i
$523$	−1.57962	−	1.57962i	−0.0690720	−	0.0690720i	0.671727	−	0.740799i	$-0.265553\pi$
$523$	−1.57962	−	1.57962i	−0.0690720	−	0.0690720i	−0.740799	+	0.671727i	$0.765553\pi$
$524$	−17.4332	+	2.33743i	−0.761574	+	0.102111i
$525$	−2.09201	+	3.90883i	−0.0913028	+	0.170595i
$526$	−11.2884	−	9.87589i	−0.492198	−	0.430609i
$527$	−13.5066	+	13.5066i	−0.588356	+	0.588356i
$528$	15.9305	−	8.89886i	0.693286	−	0.387273i
$529$			14.2991i			0.621698i
$530$	−2.87739	+	0.266070i	−0.124986	+	0.0115574i
$531$	6.89403	+	13.0594i	0.299176	+	0.566731i
$532$	−0.547068	−	0.417711i	−0.0237184	−	0.0181101i
$533$	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
$537$	−0.242633	−	0.979354i	−0.0104704	−	0.0422622i
$538$	−1.99647	−	29.9137i	−0.0860740	−	1.28967i
$539$			17.7463i			0.764388i
$540$	−23.1171	+	2.36671i	−0.994800	+	0.101847i
$541$		−	38.6062i		−	1.65981i	−0.557903	−	0.829906i	$-0.688394\pi$
$541$		−	38.6062i		−	1.65981i	0.557903	−	0.829906i	$-0.311606\pi$
$542$	−20.7072	+	1.38202i	−0.889452	+	0.0593629i
$543$	−1.54707	−	6.24454i	−0.0663912	−	0.267979i
$544$	−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	$-0.580103\pi$
$547$	16.8276	−	16.8276i	0.719498	−	0.719498i	0.968502	+	0.249005i	$0.0801034\pi$
$548$	2.55446	−	3.34552i	0.109121	−	0.142914i
$549$	8.50384	+	16.1089i	0.362935	+	0.687511i
$550$	−2.18829	−	18.4947i	−0.0933090	−	0.788618i
$551$		−	3.20052i		−	0.136347i
$552$	28.1806	+	10.0515i	1.19945	+	0.427819i
$553$	−1.47586	+	1.47586i	−0.0627597	+	0.0627597i
$554$	−11.5833	+	13.2401i	−0.492129	+	0.562517i
$555$	−14.9006	+	4.09856i	−0.632494	+	0.173974i
$556$	−26.3696	+	3.53561i	−1.11832	+	0.149943i
$557$	15.9467	+	15.9467i	0.675684	+	0.675684i	0.959020	−	0.283337i	$-0.0914414\pi$
$557$	15.9467	+	15.9467i	0.675684	+	0.675684i	−0.283337	+	0.959020i	$0.591441\pi$
$558$	13.5003	−	8.32098i	0.571515	−	0.352255i
$559$		−	52.9651i		−	2.24019i
$560$	−1.31869	−	4.38484i	−0.0557247	−	0.185294i
$561$	−12.0361	+	19.9641i	−0.508165	+	0.842884i
$562$	−0.0462237	−	0.692584i	−0.00194983	−	0.0292149i
$563$	−2.27954	+	2.27954i	−0.0960712	+	0.0960712i	−0.753509	−	0.657438i	$-0.771640\pi$
$563$	−2.27954	+	2.27954i	−0.0960712	+	0.0960712i	0.657438	+	0.753509i	$0.271640\pi$
$564$	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
$567$	−4.52787	+	0.852186i	−0.190153	+	0.0357885i
$568$	4.85156	+	23.9426i	0.203567	+	1.00461i
$569$	38.0835			1.59654			0.798272	−	0.602297i	$-0.205748\pi$
$569$	38.0835			1.59654			0.798272	+	0.602297i	$0.205748\pi$
$570$	−3.31505	−	1.60271i	−0.138852	−	0.0671303i
$571$			39.4382i			1.65044i	0.564815	+	0.825218i	$0.308948\pi$
$571$			39.4382i			1.65044i	−0.564815	+	0.825218i	$0.691052\pi$
$572$	20.6861	+	15.7948i	0.864931	+	0.660414i
$573$	9.35070	+	37.7429i	0.390631	+	1.57673i
$574$	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	0.953476	−	0.301469i	$-0.0974770\pi$
$577$	15.6617	+	15.6617i	0.652007	+	0.652007i	−0.301469	+	0.953476i	$0.597477\pi$
$578$	−0.858246	−	12.8594i	−0.0356983	−	0.534879i
$579$	−10.1353	+	16.8112i	−0.421208	+	0.698650i
$580$	12.4840	−	17.2469i	0.518370	−	0.716137i
$581$	−6.18200			−0.256473
$582$	2.03490	+	1.04881i	0.0843494	+	0.0434744i
$583$	1.70183	−	1.70183i	0.0704824	−	0.0704824i
$584$	−25.0348	+	37.7589i	−1.03595	+	1.56248i
$585$	−16.2175	−	28.9061i	−0.670512	−	1.19512i
$586$	−5.28492	+	6.04081i	−0.218318	+	0.249544i
$587$	−8.03380	−	8.03380i	−0.331590	−	0.331590i	0.521600	−	0.853190i	$-0.325335\pi$
$587$	−8.03380	−	8.03380i	−0.331590	−	0.331590i	−0.853190	+	0.521600i	$0.825335\pi$
$588$	8.57391	+	21.7091i	0.353582	+	0.895267i
$589$	2.51288			0.103541
$590$	−9.94673	+	11.9737i	−0.409501	+	0.492949i
$591$	−3.14255	−	1.89461i	−0.129267	−	0.0779338i
$592$	7.91438	−	13.8604i	0.325279	−	0.569657i
$593$	15.7097	+	15.7097i	0.645122	+	0.645122i	0.951810	−	0.306688i	$-0.0992209\pi$
$593$	15.7097	+	15.7097i	0.645122	+	0.645122i	−0.306688	+	0.951810i	$0.599221\pi$
$594$	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
$597$	−5.25482	−	21.2104i	−0.215066	−	0.868083i
$598$	2.84184	+	42.5801i	0.116211	+	1.74123i
$599$	16.2242			0.662902			0.331451	−	0.943473i	$-0.392462\pi$
$599$	16.2242			0.662902			0.331451	+	0.943473i	$0.392462\pi$
$600$	−11.6124	−	21.5674i	−0.474076	−	0.880484i
$601$	30.2446			1.23370			0.616852	−	0.787079i	$-0.288408\pi$
$601$	30.2446			1.23370			0.616852	+	0.787079i	$0.288408\pi$
$602$	−0.516815	−	7.74359i	−0.0210638	−	0.315605i
$603$	0.437230	−	1.41503i	0.0178054	−	0.0576247i
$604$	−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	0.996238	+	0.0866645i	$0.0276208\pi$
$607$	26.6799	+	26.6799i	1.08290	+	1.08290i	0.0866645	+	0.996238i	$0.472379\pi$
$608$	3.59374	−	1.24385i	0.145745	−	0.0504448i
$609$	2.17954	−	3.61516i	0.0883194	−	0.146494i
$610$	−12.2694	+	14.7697i	−0.496772	+	0.598006i
$611$	6.90044			0.279162
$612$	−5.07837	+	30.2371i	−0.205281	+	1.22226i
$613$	−11.2416	−	11.2416i	−0.454046	−	0.454046i	0.442649	−	0.896695i	$-0.354039\pi$
$613$	−11.2416	−	11.2416i	−0.454046	−	0.454046i	−0.896695	+	0.442649i	$0.854039\pi$
$614$	−10.5469	+	12.0554i	−0.425637	+	0.486515i
$615$	7.84888	−	13.8050i	0.316497	−	0.556672i
$616$	3.17847	+	2.10738i	0.128064	+	0.0849088i
$617$	15.8402	−	15.8402i	0.637702	−	0.637702i	−0.312286	−	0.949988i	$-0.601095\pi$
$617$	15.8402	−	15.8402i	0.637702	−	0.637702i	0.949988	+	0.312286i	$0.101095\pi$
$618$	−13.7882	+	26.7521i	−0.554645	+	1.07613i
$619$	39.2267			1.57665			0.788327	−	0.615256i	$-0.210948\pi$
$619$	39.2267			1.57665			0.788327	+	0.615256i	$0.210948\pi$
$620$	13.5413	+	9.80178i	0.543832	+	0.393649i
$621$	31.6832	+	1.80234i	1.27140	+	0.0723254i
$622$	−1.21369	−	18.1851i	−0.0486645	−	0.729156i
$623$	−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
$627$	2.97679	−	0.737493i	0.118882	−	0.0294526i
$628$	23.9487	−	31.3652i	0.955658	−	1.25161i
$629$			20.3903i			0.813016i
$630$	−2.65309	−	4.06788i	−0.105701	−	0.162068i
$631$	9.52029			0.378997			0.189498	−	0.981881i	$-0.439314\pi$
$631$	9.52029			0.378997			0.189498	+	0.981881i	$0.439314\pi$
$632$	−2.29016	−	11.3020i	−0.0910977	−	0.449569i
$633$	−5.83166	−	23.5387i	−0.231788	−	0.935580i
$634$	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
$638$	1.18088	+	17.6934i	0.0467513	+	0.700489i
$639$	12.0963	+	22.9142i	0.478524	+	0.906472i
$640$	24.2176	+	7.31497i	0.957284	+	0.289150i
$641$			42.2578i			1.66908i	0.550945	+	0.834541i	$0.314267\pi$
$641$			42.2578i			1.66908i	−0.550945	+	0.834541i	$0.685733\pi$
$642$	−9.57522	−	4.93515i	−0.377904	−	0.194775i
$643$	−15.1060	−	15.1060i	−0.595722	−	0.595722i	0.343449	−	0.939171i	$-0.388405\pi$
$643$	−15.1060	−	15.1060i	−0.595722	−	0.595722i	−0.939171	+	0.343449i	$0.888405\pi$
$644$	0.830963	+	6.19756i	0.0327445	+	0.244218i
$645$	−11.0108	−	40.0304i	−0.433550	−	1.57620i
$646$	−3.19895	+	3.65649i	−0.125861	+	0.143863i
$647$	11.1088	−	11.1088i	0.436732	−	0.436732i	−0.454178	−	0.890911i	$-0.650067\pi$
$647$	11.1088	−	11.1088i	0.436732	−	0.436732i	0.890911	+	0.454178i	$0.150067\pi$
$648$	9.89982	−	23.4519i	0.388902	−	0.921279i
$649$		−	12.9648i		−	0.508912i
$650$	21.6307	−	27.4363i	0.848426	−	1.07614i
$651$	2.83843	+	1.71126i	0.111247	+	0.0670695i
$652$	14.9817	+	11.4392i	0.586729	+	0.447995i
$653$	−15.4673	+	15.4673i	−0.605283	+	0.605283i	−0.941710	−	0.336426i	$-0.890782\pi$
$653$	−15.4673	+	15.4673i	−0.605283	+	0.605283i	0.336426	+	0.941710i	$0.390782\pi$
$654$	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
$657$	−14.1859	+	45.9108i	−0.553445	+	1.79115i
$658$	1.00886	−	0.0673320i	0.0393293	−	0.00262487i
$659$		−	5.93274i		−	0.231107i	−0.993301	−	0.115553i	$-0.963136\pi$
$659$		−	5.93274i		−	0.231107i	0.993301	−	0.115553i	$-0.0368641\pi$
$660$	18.9179	+	7.63714i	0.736378	+	0.297275i
$661$		−	28.1054i		−	1.09317i	−0.837403	−	0.546586i	$-0.815927\pi$
$661$		−	28.1054i		−	1.09317i	0.837403	−	0.546586i	$-0.184073\pi$
$662$	−2.09406	−	31.3760i	−0.0813881	−	1.21946i
$663$	−42.4486	+	10.5165i	−1.64857	+	0.408429i
$664$	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
$668$	26.8553	−	35.1719i	1.03906	−	1.36084i
$669$	3.24434	−	5.38133i	0.125433	−	0.208054i
$670$	1.55453	−	0.143746i	0.0600566	−	0.00555339i
$671$		−	15.9922i		−	0.617370i
$672$	4.90638	+	1.04232i	0.189268	+	0.0402084i
$673$	−15.2277	+	15.2277i	−0.586986	+	0.586986i	−0.936814	−	0.349828i	$-0.886240\pi$
$673$	−15.2277	+	15.2277i	−0.586986	+	0.586986i	0.349828	+	0.936814i	$0.386240\pi$
$674$	−13.5276	−	11.8349i	−0.521063	−	0.455862i
$675$	−18.2662	−	18.4755i	−0.703068	−	0.711122i
$676$	3.03327	+	22.6230i	0.116664	+	0.870116i
$677$	−28.2327	−	28.2327i	−1.08507	−	1.08507i	−0.996028	−	0.0890415i	$-0.971620\pi$
$677$	−28.2327	−	28.2327i	−1.08507	−	1.08507i	−0.0890415	−	0.996028i	$-0.528380\pi$
$678$	13.4951	+	6.95547i	0.518275	+	0.267123i
$679$			0.478448i			0.0183611i
$680$	−31.5010	+	7.22608i	−1.20801	+	0.277108i
$681$	28.0352	+	16.9021i	1.07431	+	0.647691i
$682$	−13.8919	+	0.927161i	−0.531950	+	0.0355028i
$683$	−26.1080	+	26.1080i	−0.998996	+	0.998996i	−0.999999	−	0.00100333i	$-0.999681\pi$
$683$	−26.1080	+	26.1080i	−0.998996	+	0.998996i	0.00100333	+	0.999999i	$0.499681\pi$
$684$	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
$687$	−26.4971	+	6.56460i	−1.01093	+	0.250455i
$688$	37.2359	+	21.2620i	1.41961	+	0.810607i
$689$	4.51498			0.172007
$690$	10.9997	+	31.5908i	0.418752	+	1.20264i
$691$		−	9.65683i		−	0.367363i	−0.982986	−	0.183682i	$-0.941198\pi$
$691$		−	9.65683i		−	0.367363i	0.982986	−	0.183682i	$-0.0588015\pi$
$692$	−10.9912	+	14.3949i	−0.417822	+	0.547213i
$693$	3.86468	+	1.19414i	0.146807	+	0.0453617i
$694$	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
$698$	−24.8234	+	1.65674i	−0.939580	+	0.0627085i
$699$	−27.3120	−	16.4661i	−1.03303	−	0.622804i
$700$	2.89473	−	4.22230i	0.109411	−	0.159588i
$701$	22.2509			0.840403			0.420202	−	0.907431i	$-0.361959\pi$
$701$	22.2509			0.840403			0.420202	+	0.907431i	$0.361959\pi$
$702$	36.3065	−	0.356434i	1.37030	−	0.0134527i
$703$	1.89679	−	1.89679i	0.0715390	−	0.0715390i
$704$	−19.4083	+	8.20233i	−0.731478	+	0.309137i
$705$	5.21527	−	1.43452i	0.196419	−	0.0540270i
$706$	−19.5161	−	17.0741i	−0.734499	−	0.642591i
$707$	1.25556	+	1.25556i	0.0472202	+	0.0472202i
$708$	−6.26377	−	15.8598i	−0.235407	−	0.596048i
$709$	−22.1309			−0.831144			−0.415572	−	0.909560i	$-0.636419\pi$
$709$	−22.1309			−0.831144			−0.415572	+	0.909560i	$0.636419\pi$
$710$	−17.4527	+	21.0092i	−0.654986	+	0.788461i
$711$	−5.71003	−	10.8166i	−0.214143	−	0.405653i
$712$	18.2565	−	3.69938i	0.684192	−	0.138640i
$713$	−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
$717$	41.7509	−	10.3437i	1.55922	−	0.386292i
$718$	−23.3172	+	1.55621i	−0.870189	+	0.0580772i
$719$	−4.65932			−0.173763			−0.0868817	−	0.996219i	$-0.527690\pi$
$719$	−4.65932			−0.173763			−0.0868817	+	0.996219i	$0.527690\pi$
$720$	26.8321	+	0.202570i	0.999972	+	0.00754934i
$721$	−6.28997			−0.234251
$722$	−26.1727	+	1.74679i	−0.974047	+	0.0650088i
$723$	−29.0836	+	7.20539i	−1.08163	+	0.267971i
$724$	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	−0.997358	−	0.0726443i	$-0.976856\pi$
$727$	−28.8504	−	28.8504i	−1.07000	−	1.07000i	−0.0726443	−	0.997358i	$-0.523144\pi$
$728$	1.42081	+	7.01174i	0.0526588	+	0.259872i
$729$	3.06195	−	26.8258i	0.113406	−	0.993549i
$730$	−50.4366	+	4.66383i	−1.86674	+	0.172616i
$731$	−54.7787			−2.02606
$732$	−7.72641	−	19.5632i	−0.285576	−	0.723077i
$733$	−23.8359	−	23.8359i	−0.880398	−	0.880398i	0.113177	−	0.993575i	$-0.463897\pi$
$733$	−23.8359	−	23.8359i	−0.880398	−	0.880398i	−0.993575	+	0.113177i	$0.963897\pi$
$734$	−36.8636	−	32.2508i	−1.36066	−	1.19040i
$735$	−12.8980	+	22.6856i	−0.475749	+	0.836772i
$736$	−31.0758	−	15.0952i	−1.14547	−	0.556418i
$737$	−0.919420	+	0.919420i	−0.0338673	+	0.0338673i
$738$	9.12759	+	14.8090i	0.335991	+	0.545128i
$739$	−29.6476			−1.09060			−0.545302	−	0.838240i	$-0.683585\pi$
$739$	−29.6476			−1.09060			−0.545302	+	0.838240i	$0.683585\pi$
$740$	17.6200	−	2.82271i	0.647726	−	0.103765i
$741$	4.92704	+	2.97046i	0.180999	+	0.109122i
$742$	0.660098	−	0.0440556i	0.0242330	−	0.00161733i
$743$	8.41878	+	8.41878i	0.308855	+	0.308855i	0.844465	−	0.535610i	$-0.179918\pi$
$743$	8.41878	+	8.41878i	0.308855	+	0.308855i	−0.535610	+	0.844465i	$0.679918\pi$
$744$	−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
$747$	10.6950	−	34.6130i	0.391310	−	1.26642i
$748$	16.3356	−	21.3945i	0.597290	−	0.782259i
$749$		−	2.25134i		−	0.0822620i
$750$	10.6446	−	25.2328i	0.388685	−	0.921371i
$751$	−31.5577			−1.15156			−0.575778	−	0.817606i	$-0.695301\pi$
$751$	−31.5577			−1.15156			−0.575778	+	0.817606i	$0.695301\pi$
$752$	−2.77007	+	4.85119i	−0.101014	+	0.176905i
$753$	1.76583	−	0.437480i	0.0643503	−	0.0159426i
$754$	−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	$-0.977610\pi$
$757$	−25.5118	+	25.5118i	−0.927244	+	0.927244i	0.0702832	+	0.997527i	$0.477610\pi$
$758$	−8.08698	+	0.539733i	−0.293732	+	0.0196040i
$759$	−23.8599	−	14.3848i	−0.866059	−	0.522137i
$760$	3.60255	+	2.25815i	0.130678	+	0.0819118i
$761$			2.30287i			0.0834789i	0.999129	+	0.0417394i	$0.0132899\pi$
$761$			2.30287i			0.0834789i	−0.999129	+	0.0417394i	$0.986710\pi$
$762$	−30.4439	−	15.6910i	−1.10286	−	0.568426i
$763$	1.49979	+	1.49979i	0.0542962	+	0.0542962i
$764$	−5.96666	−	44.5011i	−0.215866	−	1.60999i
$765$	−29.8959	+	16.7728i	−1.08089	+	0.606423i
$766$	25.9810	+	22.7300i	0.938733	+	0.821269i
$767$	17.1979	−	17.1979i	0.620981	−	0.620981i
$768$	−19.7793	+	19.4108i	−0.713725	+	0.700426i
$769$			46.5571i			1.67889i	0.543442	+	0.839447i	$0.317121\pi$
$769$			46.5571i			1.67889i	−0.543442	+	0.839447i	$0.682879\pi$
$770$	0.392592	+	4.24565i	0.0141480	+	0.153003i
$771$	2.78633	−	4.62164i	0.100347	−	0.166444i
$772$	13.7558	−	18.0157i	0.495082	−	0.648399i
$773$	19.2506	−	19.2506i	0.692397	−	0.692397i	−0.270362	−	0.962759i	$-0.587143\pi$
$773$	19.2506	−	19.2506i	0.692397	−	0.692397i	0.962759	+	0.270362i	$0.0871434\pi$
$774$	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
$777$	3.43424	−	0.850825i	0.123203	−	0.0305232i
$778$	2.63035	+	39.4113i	0.0943024	+	1.41296i
$779$			2.75647i			0.0987608i
$780$	14.9641	+	35.2256i	0.535799	+	1.26128i
$781$		−	22.7481i		−	0.813993i
$782$	44.0381	−	2.93914i	1.57480	−	0.105104i
$783$	16.4706	+	18.4575i	0.588611	+	0.659618i
$784$	−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	$-0.780488\pi$
$787$	−3.79411	+	3.79411i	−0.135246	+	0.135246i	0.636243	+	0.771489i	$0.280488\pi$
$788$	3.36771	+	2.57140i	0.119970	+	0.0916023i
$789$	15.7317	+	9.48447i	0.560064	+	0.337656i
$790$	8.23845	−	9.91730i	0.293111	−	0.352842i
$791$			3.17297i			0.112818i
$792$	−17.2980	+	14.1504i	−0.614659	+	0.502812i
$793$	21.2138	−	21.2138i	0.753324	−	0.753324i
$794$	−4.16445	+	4.76008i	−0.147791	+	0.168929i
$795$	3.41237	−	0.938610i	0.121024	−	0.0332891i
$796$	3.35309	+	25.0083i	0.118847	+	0.886396i
$797$	30.0747	+	30.0747i	1.06530	+	1.06530i	0.997713	+	0.0675880i	$0.0215303\pi$
$797$	30.0747	+	30.0747i	1.06530	+	1.06530i	0.0675880	+	0.997713i	$0.478470\pi$
$798$	0.749327	+	0.386209i	0.0265259	+	0.0136717i
$799$		−	7.13671i		−	0.252479i
$800$	10.6051	+	26.2208i	0.374948	+	0.927046i
$801$	17.4724	−	9.22362i	0.617356	−	0.325901i
$802$	−1.05977	−	15.8789i	−0.0374218	−	0.560702i
$803$	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
$807$	8.82990	+	35.6407i	0.310827	+	1.25461i
$808$	−9.61499	+	1.94832i	−0.338254	+	0.0685416i
$809$	−21.7890			−0.766061			−0.383031	−	0.923736i	$-0.625120\pi$
$809$	−21.7890			−0.766061			−0.383031	+	0.923736i	$0.625120\pi$
$810$	27.3659	−	7.81706i	0.961540	−	0.274663i
$811$			2.48698i			0.0873295i	0.999046	+	0.0436648i	$0.0139033\pi$
$811$			2.48698i			0.0873295i	−0.999046	+	0.0436648i	$0.986097\pi$
$812$	−2.95811	+	3.87418i	−0.103809	+	0.135957i
$813$	24.6716	−	6.11234i	0.865272	−	0.214369i
$814$	−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
$818$	−0.476499	−	7.13954i	−0.0166604	−	0.249628i
$819$	3.54250	+	6.71058i	0.123785	+	0.234487i
$820$	−10.7519	+	14.8540i	−0.375474	+	0.518723i
$821$	−7.50855			−0.262050			−0.131025	−	0.991379i	$-0.541827\pi$
$821$	−7.50855			−0.262050			−0.131025	+	0.991379i	$0.541827\pi$
$822$	−2.36181	+	4.58241i	−0.0823777	+	0.159830i
$823$	33.8234	−	33.8234i	1.17901	−	1.17901i	0.199012	−	0.979997i	$-0.436227\pi$
$823$	33.8234	−	33.8234i	1.17901	−	1.17901i	0.979997	−	0.199012i	$-0.0637733\pi$
$824$	19.2038	−	28.9643i	0.668997	−	1.00902i
$825$	6.60949	+	21.8307i	0.230113	+	0.760048i
$826$	2.34656	−	2.68218i	0.0816471	−	0.0933249i
$827$	20.6186	+	20.6186i	0.716979	+	0.716979i	0.967985	−	0.251007i	$-0.0807616\pi$
$827$	20.6186	+	20.6186i	0.716979	+	0.716979i	−0.251007	+	0.967985i	$0.580762\pi$
$828$	−36.1376	−	6.06937i	−1.25587	−	0.210925i
$829$	−16.9499			−0.588694			−0.294347	−	0.955699i	$-0.595102\pi$
$829$	−16.9499			−0.588694			−0.294347	+	0.955699i	$0.595102\pi$
$830$	38.0250	−	3.51615i	1.31987	−	0.122047i
$831$	11.1243	−	18.4516i	0.385896	−	0.640079i
$832$	−36.6258	−	14.8649i	−1.26977	−	0.515346i
$833$	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
$837$	−14.4919	+	12.9318i	−0.500912	+	0.446990i
$838$	−2.37157	−	35.5340i	−0.0819246	−	1.22750i
$839$	31.3869			1.08360			0.541798	−	0.840509i	$-0.317744\pi$
$839$	31.3869			1.08360			0.541798	+	0.840509i	$0.317744\pi$
$840$	2.53149	+	5.00402i	0.0873447	+	0.172655i
$841$	6.33479			0.218441
$842$	2.96742	+	44.4617i	0.102264	+	1.53225i
$843$	0.204436	+	0.825179i	0.00704116	+	0.0284207i
$844$	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
$848$	−1.81247	+	3.17415i	−0.0622405	+	0.109001i
$849$	19.7966	+	11.9351i	0.679418	+	0.409613i
$850$	−28.3757	−	22.3713i	−0.973279	−	0.767331i
$851$	−24.3693			−0.835369
$852$	−10.9905	−	27.8278i	−0.376528	−	0.953365i
$853$	4.93576	+	4.93576i	0.168997	+	0.168997i	0.786538	−	0.617541i	$-0.211871\pi$
$853$	4.93576	+	4.93576i	0.168997	+	0.168997i	−0.617541	+	0.786538i	$0.711871\pi$
$854$	2.89449	−	3.30849i	0.0990476	−	0.113214i
$855$	4.34132	+	1.22076i	0.148470	+	0.0417493i
$856$	10.3670	+	6.87353i	0.354338	+	0.234932i
$857$	−23.9182	+	23.9182i	−0.817029	+	0.817029i	−0.985676	−	0.168648i	$-0.946060\pi$
$857$	−23.9182	+	23.9182i	−0.817029	+	0.817029i	0.168648	+	0.985676i	$0.446060\pi$
$858$	−28.3341	−	14.6037i	−0.967311	−	0.498560i
$859$	22.2708			0.759871			0.379935	−	0.925013i	$-0.375946\pi$
$859$	22.2708			0.759871			0.379935	+	0.925013i	$0.375946\pi$
$860$	7.58322	+	47.3363i	0.258586	+	1.61416i
$861$	−1.87714	+	3.11358i	−0.0639728	+	0.106111i
$862$	1.28157	+	19.2021i	0.0436503	+	0.654027i
$863$	−37.8907	−	37.8907i	−1.28982	−	1.28982i	−0.934897	−	0.354918i	$-0.884509\pi$
$863$	−37.8907	−	37.8907i	−1.28982	−	1.28982i	−0.354918	−	0.934897i	$-0.615491\pi$
$864$	−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
$867$	3.79581	+	15.3213i	0.128912	+	0.520338i
$868$	−3.04180	−	2.32255i	−0.103245	−	0.0788326i
$869$			10.7382i			0.364267i
$870$	−11.3500	+	23.4763i	−0.384800	+	0.795919i
$871$	−2.43924			−0.0826506
$872$	−11.4853	+	2.32731i	−0.388942	+	0.0788125i
$873$	−2.67882	−	0.827726i	−0.0906645	−	0.0280143i
$874$	−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	$-0.595855\pi$
$877$	19.4977	−	19.4977i	0.658392	−	0.658392i	0.954999	+	0.296608i	$0.0958553\pi$
$878$	−0.524185	−	7.85403i	−0.0176904	−	0.265061i
$879$	5.07546	−	8.41857i	0.171191	−	0.283951i
$880$	−20.7491	−	11.1545i	−0.699454	−	0.376019i
$881$		−	36.8489i		−	1.24147i	−0.784021	−	0.620735i	$-0.786834\pi$
$881$		−	36.8489i		−	1.24147i	0.784021	−	0.620735i	$-0.213166\pi$
$882$	−14.9993	−	24.3355i	−0.505052	−	0.819419i
$883$	25.6982	+	25.6982i	0.864813	+	0.864813i	0.991893	−	0.127079i	$-0.0405602\pi$
$883$	25.6982	+	25.6982i	0.864813	+	0.864813i	−0.127079	+	0.991893i	$0.540560\pi$
$884$	50.0494	−	6.71058i	1.68334	−	0.225701i
$885$	9.42276	−	16.5732i	0.316743	−	0.557103i
$886$	−4.65458	+	5.32031i	−0.156374	+	0.178739i
$887$	−19.3369	+	19.3369i	−0.649270	+	0.649270i	−0.952817	−	0.303547i	$-0.901829\pi$
$887$	−19.3369	+	19.3369i	−0.649270	+	0.649270i	0.303547	+	0.952817i	$0.401829\pi$
$888$	−6.56712	+	18.4118i	−0.220378	+	0.617858i
$889$		−	7.15799i		−	0.240071i
$890$	16.0198	+	13.3079i	0.536984	+	0.446081i
$891$	−13.3720	+	19.5724i	−0.447978	+	0.655699i
$892$	−4.40328	+	5.76689i	−0.147433	+	0.193090i
$893$	−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
$897$	−12.5688	−	50.7321i	−0.419658	−	1.69389i
$898$	29.9000	−	1.99555i	0.997775	−	0.0665925i
$899$		−	17.7955i		−	0.593514i
$900$	18.6326	+	23.5122i	0.621088	+	0.783741i
$901$		−	4.66958i		−	0.155566i
$902$	−1.01704	−	15.2386i	−0.0338636	−	0.507389i
$903$	2.28574	+	9.22610i	0.0760648	+	0.307025i
$904$	−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	$-0.879500\pi$
$907$	−16.8535	+	16.8535i	−0.559613	+	0.559613i	0.369585	+	0.929197i	$0.379500\pi$
$908$	−30.0439	−	22.9399i	−0.997042	−	0.761287i
$909$	−9.20201	+	4.85772i	−0.305212	+	0.161120i
$910$	−5.11112	+	6.15268i	−0.169432	+	0.203959i
$911$			31.3998i			1.04032i	0.854068	+	0.520161i	$0.174128\pi$
$911$			31.3998i			1.04032i	−0.854068	+	0.520161i	$0.825872\pi$
$912$	−4.06619	+	2.27140i	−0.134645	+	0.0752135i
$913$	−22.4898	+	22.4898i	−0.744304	+	0.744304i
$914$	25.4071	+	22.2279i	0.840393	+	0.735234i
$915$	11.6230	−	20.4432i	0.384246	−	0.675832i
$916$	31.2417	−	4.18886i	1.03225	−	0.138404i
$917$	3.18356	+	3.18356i	0.105130	+	0.105130i
$918$	−0.368638	−	37.5496i	−0.0121669	−	1.23932i
$919$			26.0422i			0.859054i	0.903054	+	0.429527i	$0.141320\pi$
$919$			26.0422i			0.859054i	−0.903054	+	0.429527i	$0.858680\pi$
$920$	−8.63619	−	37.6481i	−0.284727	−	1.24122i
$921$	10.1289	−	16.8006i	0.333757	−	0.553597i
$922$	5.06414	−	0.337986i	0.166779	−	0.0111310i
$923$	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
$927$	10.8818	−	35.2175i	0.357405	−	1.15669i
$928$	−8.80860	−	25.4499i	−0.289157	−	0.835433i
$929$	−16.2184			−0.532108			−0.266054	−	0.963958i	$-0.585720\pi$
$929$	−16.2184			−0.532108			−0.266054	+	0.963958i	$0.585720\pi$
$930$	−18.4323	−	8.91140i	−0.604419	−	0.292216i
$931$		−	4.52968i		−	0.148454i
$932$	29.2688	+	22.3481i	0.958733	+	0.732036i
$933$	5.36785	+	21.6666i	0.175736	+	0.709333i
$934$	−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	0.432557	−	0.901607i	$-0.357611\pi$
$937$	−14.3578	−	14.3578i	−0.469050	−	0.469050i	−0.901607	+	0.432557i	$0.857611\pi$
$938$	−0.356621	+	0.0238012i	−0.0116441	+	0.000777138i
$939$	−15.5547	+	25.8002i	−0.507607	+	0.841959i
$940$	−6.16710	+	0.987962i	−0.201149	+	0.0322238i
$941$	−27.3264			−0.890817			−0.445408	−	0.895328i	$-0.646941\pi$
$941$	−27.3264			−0.890817			−0.445408	+	0.895328i	$0.646941\pi$
$942$	−22.1426	+	42.9613i	−0.721446	+	1.39976i
$943$	17.7071	−	17.7071i	0.576621	−	0.576621i
$944$	5.18676	+	18.9944i	0.168815	+	0.618216i
$945$	4.07242	+	4.33534i	0.132476	+	0.141029i
$946$	−30.0509	−	26.2906i	−0.977040	−	0.854783i
$947$	17.5336	+	17.5336i	0.569766	+	0.569766i	0.932063	−	0.362297i	$-0.118007\pi$
$947$	17.5336	+	17.5336i	0.569766	+	0.569766i	−0.362297	+	0.932063i	$0.618007\pi$
$948$	5.18801	+	13.1360i	0.168499	+	0.426637i
$949$	79.1412			2.56903
$950$	0.558552	+	4.72071i	0.0181218	+	0.153160i
$951$	−19.3868	−	11.6881i	−0.628661	−	0.379012i
$952$	7.25183	−	1.46946i	0.235033	−	0.0476255i
$953$	−19.5859	−	19.5859i	−0.634449	−	0.634449i	0.314732	−	0.949181i	$-0.398085\pi$
$953$	−19.5859	−	19.5859i	−0.634449	−	0.634449i	−0.949181	+	0.314732i	$0.898085\pi$
$954$	−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
$957$	−5.22272	−	21.0808i	−0.168827	−	0.681446i
$958$	3.65252	−	0.243772i	0.118008	−	0.00787593i
$959$	−1.07742			−0.0347917
$960$	−30.7716	−	3.62063i	−0.993149	−	0.116855i
$961$	−17.0279			−0.549287
$962$	−27.8197	+	1.85671i	−0.896943	+	0.0598628i
$963$	12.6052	+	3.89486i	0.406197	+	0.125510i
$964$	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	0.399332	−	0.916806i	$-0.369242\pi$
$967$	−16.0917	−	16.0917i	−0.517475	−	0.517475i	−0.916806	+	0.399332i	$0.869242\pi$
$968$	−11.2633	+	2.28232i	−0.362017	+	0.0733567i
$969$	3.07217	−	5.09575i	0.0986922	−	0.163699i
$970$	−0.272128	−	2.94290i	−0.00873749	−	0.0944907i
$971$	56.1374			1.80154			0.900768	−	0.434301i	$-0.143005\pi$
$971$	56.1374			1.80154			0.900768	+	0.434301i	$0.143005\pi$
$972$	−6.90177	+	30.4034i	−0.221374	+	0.975189i
$973$	4.81546	+	4.81546i	0.154377	+	0.154377i
$974$	12.4932	+	10.9299i	0.400308	+	0.350217i
$975$	−20.1912	+	37.7263i	−0.646635	+	1.20821i
$976$	6.39791	+	23.4298i	0.204792	+	0.749969i
$977$	1.50786	−	1.50786i	0.0482409	−	0.0482409i	−0.682575	−	0.730816i	$-0.739140\pi$
$977$	1.50786	−	1.50786i	0.0482409	−	0.0482409i	0.730816	+	0.682575i	$0.239140\pi$
$978$	−20.5207	−	10.5765i	−0.656179	−	0.338200i
$979$	−17.3458			−0.554373
$980$	17.6685	−	24.4094i	0.564400	−	0.779728i
$981$	−10.9920	+	5.80265i	−0.350948	+	0.185264i
$982$	35.7993	−	2.38928i	1.14240	−	0.0762450i
$983$	20.1605	+	20.1605i	0.643021	+	0.643021i	0.951297	−	0.308276i	$-0.0997519\pi$
$983$	20.1605	+	20.1605i	0.643021	+	0.643021i	−0.308276	+	0.951297i	$0.599752\pi$
$984$	−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
$987$	−1.20200	+	0.297793i	−0.0382601	+	0.00947885i
$988$	−5.28006	−	4.03156i	−0.167981	−	0.128261i
$989$		−	65.4683i		−	2.08177i
$990$	−24.4505	−	5.14695i	−0.777089	−	0.163581i
$991$	36.8471			1.17049			0.585244	−	0.810858i	$-0.300999\pi$
$991$	36.8471			1.17049			0.585244	+	0.810858i	$0.300999\pi$
$992$	19.9819	−	6.91605i	0.634425	−	0.219585i
$993$	9.26153	+	37.3829i	0.293906	+	1.18631i
$994$	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	$-0.966879\pi$
$997$	−28.1250	+	28.1250i	−0.890726	+	0.890726i	0.103865	+	0.994591i	$0.466879\pi$
$998$	40.4614	−	2.70043i	1.28078	−	0.0854806i
$999$	−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.77.16	yes	32
3.2	odd	2	inner	120.2.w.c.77.1	yes	32
4.3	odd	2		480.2.bi.c.17.15		32
5.2	odd	4		600.2.w.j.293.9		32
5.3	odd	4	inner	120.2.w.c.53.8	yes	32
5.4	even	2		600.2.w.j.557.1		32
8.3	odd	2		480.2.bi.c.17.2		32
8.5	even	2	inner	120.2.w.c.77.9	yes	32
12.11	even	2		480.2.bi.c.17.7		32
15.2	even	4		600.2.w.j.293.8		32
15.8	even	4	inner	120.2.w.c.53.9	yes	32
15.14	odd	2		600.2.w.j.557.16		32
20.3	even	4		480.2.bi.c.113.10		32
24.5	odd	2	inner	120.2.w.c.77.8	yes	32
24.11	even	2		480.2.bi.c.17.10		32
40.3	even	4		480.2.bi.c.113.7		32
40.13	odd	4	inner	120.2.w.c.53.1	✓	32
40.29	even	2		600.2.w.j.557.8		32
40.37	odd	4		600.2.w.j.293.16		32
60.23	odd	4		480.2.bi.c.113.2		32
120.29	odd	2		600.2.w.j.557.9		32
120.53	even	4	inner	120.2.w.c.53.16	yes	32
120.77	even	4		600.2.w.j.293.1		32
120.83	odd	4		480.2.bi.c.113.15		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.w.c.53.1	✓	32	40.13	odd	4	inner
120.2.w.c.53.8	yes	32	5.3	odd	4	inner
120.2.w.c.53.9	yes	32	15.8	even	4	inner
120.2.w.c.53.16	yes	32	120.53	even	4	inner
120.2.w.c.77.1	yes	32	3.2	odd	2	inner
120.2.w.c.77.8	yes	32	24.5	odd	2	inner
120.2.w.c.77.9	yes	32	8.5	even	2	inner
120.2.w.c.77.16	yes	32	1.1	even	1	trivial
480.2.bi.c.17.2		32	8.3	odd	2
480.2.bi.c.17.7		32	12.11	even	2
480.2.bi.c.17.10		32	24.11	even	2
480.2.bi.c.17.15		32	4.3	odd	2
480.2.bi.c.113.2		32	60.23	odd	4
480.2.bi.c.113.7		32	40.3	even	4
480.2.bi.c.113.10		32	20.3	even	4
480.2.bi.c.113.15		32	120.83	odd	4
600.2.w.j.293.1		32	120.77	even	4
600.2.w.j.293.8		32	15.2	even	4
600.2.w.j.293.9		32	5.2	odd	4
600.2.w.j.293.16		32	40.37	odd	4
600.2.w.j.557.1		32	5.4	even	2
600.2.w.j.557.8		32	40.29	even	2
600.2.w.j.557.9		32	120.29	odd	2
600.2.w.j.557.16		32	15.14	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:	\( N \)	\(=\)	\( 120 = 2^{3} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	120.w (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41107 - 0.0941764i) q^{2} +(-1.68122 + 0.416519i) q^{3} +(1.98226 - 0.265780i) q^{4} +(1.62104 + 1.54020i) q^{5} +(-2.33310 + 0.746071i) q^{6} +(-0.361989 - 0.361989i) q^{7} +(2.77209 - 0.561717i) q^{8} +(2.65302 - 1.40052i) q^{9} +O(q^{10})\)	\(q+(1.41107 - 0.0941764i) q^{2} +(-1.68122 + 0.416519i) 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} +(2.77209 - 0.561717i) q^{8} +(2.65302 - 1.40052i) q^{9} +(2.43246 + 2.02068i) q^{10} -2.63380 q^{11} +(-3.22192 + 1.27249i) q^{12} +(-3.49376 - 3.49376i) q^{13} +(-0.544885 - 0.476703i) q^{14} +(-3.36685 - 1.91423i) q^{15} +(3.85872 - 1.05369i) q^{16} +(-3.61339 + 3.61339i) q^{17} +(3.61172 - 2.22609i) q^{18} +0.672266 q^{19} +(3.62268 + 2.62225i) q^{20} +(0.759360 + 0.457809i) q^{21} +(-3.71648 + 0.248041i) 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} +(-3.87698 + 3.45963i) q^{27} +(-0.813767 - 0.621348i) q^{28} -4.76080i q^{29} +(-4.93116 - 2.38405i) q^{30} +3.73793 q^{31} +(5.34571 - 1.85024i) q^{32} +(4.42800 - 1.09703i) 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} +(0.948617 - 0.0633116i) q^{38} +(7.32901 + 4.41857i) q^{39} +(5.35882 + 3.35902i) q^{40} +4.10027i q^{41} +(1.11463 + 0.574489i) q^{42} +(7.57996 + 7.57996i) q^{43} +(-5.22087 + 0.700010i) q^{44} +(6.45775 + 1.81590i) q^{45} +(-6.50044 - 5.68704i) q^{46} +(-0.987537 + 0.987537i) q^{47} +(-6.04849 + 3.37872i) q^{48} -6.73793i q^{49} +(0.830850 + 7.02209i) q^{50} +(4.56987 - 7.57996i) q^{51} +(-7.85412 - 5.99698i) 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} +(-1.13023 + 0.280012i) q^{57} +(-0.448355 - 6.71784i) q^{58} +4.92247i q^{59} +(-7.18275 - 2.89967i) q^{60} +6.07190i q^{61} +(5.27449 - 0.352025i) q^{62} +(-1.46734 - 0.453392i) 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} +(-6.20232 + 8.12305i) q^{68} +(9.05912 + 5.46164i) q^{69} +(-0.149059 - 1.61199i) q^{70} +8.63702i q^{71} +(6.56772 - 5.37262i) q^{72} +(-11.3261 + 11.3261i) q^{73} +(3.71562 - 4.24706i) q^{74} +(-2.50949 - 8.28869i) q^{75} +(1.33261 - 0.178675i) q^{76} +(0.953406 + 0.953406i) q^{77} +(10.7579 + 5.54472i) q^{78} -4.07707i q^{79} +(7.87804 + 4.23515i) q^{80} +(5.07707 - 7.43124i) q^{81} +(0.386149 + 5.78579i) 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} +(1.98296 + 8.00397i) q^{87} +(-7.30111 + 1.47945i) q^{88} +6.58584 q^{89} +(9.28338 + 1.95420i) q^{90} +2.52941i q^{91} +(-9.70819 - 7.41264i) q^{92} +(-6.28429 + 1.55692i) 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} +(-0.634554 - 9.50772i) 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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