LMFDB - Embedded newform 120.2.w.c.53.1

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			53.1
Character	$\chi$	$=$	120.53
Dual form			120.2.w.c.77.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41107 - 0.0941764i) q^{2} +(0.416519 + 1.68122i) q^{3} +(1.98226 + 0.265780i) q^{4} +(-1.62104 + 1.54020i) q^{5} +(-0.429408 - 2.41156i) q^{6} +(-0.361989 + 0.361989i) q^{7} +(-2.77209 - 0.561717i) q^{8} +(-2.65302 + 1.40052i) q^{9} +O(q^{10})$	\(q+(-1.41107 - 0.0941764i) q^{2} +(0.416519 + 1.68122i) q^{3} +(1.98226 + 0.265780i) q^{4} +(-1.62104 + 1.54020i) q^{5} +(-0.429408 - 2.41156i) 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} +(0.378815 + 3.44333i) 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} +(3.87551 - 1.72639i) 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} +(-0.210256 - 4.89447i) q^{24} +(0.255538 - 4.99347i) q^{25} +(5.25899 - 4.60093i) q^{26} +(-3.45963 - 3.87698i) q^{27} +(-0.813767 + 0.621348i) q^{28} -4.76080i q^{29} +(4.41038 + 3.24785i) q^{30} +3.73793 q^{31} +(-5.34571 - 1.85024i) q^{32} +(1.09703 + 4.42800i) q^{33} +(-4.75847 - 5.43906i) q^{34} +(0.0292613 - 1.14434i) q^{35} +(-5.63122 + 2.07108i) 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} +(1.02840 + 0.717517i) 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} +(-0.164257 + 6.92626i) 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} +(4.51667 + 5.79652i) q^{54} +(-4.26949 + 4.05659i) q^{55} +(1.20680 - 0.800131i) q^{56} +(0.280012 + 1.13023i) q^{57} +(-0.448355 + 6.71784i) q^{58} +4.92247i q^{59} +(-5.91750 - 4.99832i) q^{60} -6.07190i q^{61} +(-5.27449 - 0.352025i) q^{62} +(0.453392 - 1.46734i) q^{63} +(7.36895 + 3.11426i) q^{64} +(0.282417 - 11.0446i) q^{65} +(-1.13097 - 6.35155i) 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} +(8.14111 - 2.39213i) 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} +(9.92565 + 6.92516i) 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} +(-1.38357 - 1.10932i) q^{84} +(-11.4228 - 0.292087i) q^{85} +(-11.4097 + 9.98203i) q^{86} +(8.00397 - 1.98296i) q^{87} +(-7.30111 - 1.47945i) q^{88} -6.58584 q^{89} +(-3.62336 + 8.76763i) q^{90} -2.52941i q^{91} +(9.70819 - 7.41264i) q^{92} +(1.55692 + 6.28429i) q^{93} +(-1.30049 - 1.48649i) q^{94} +(-1.08977 + 1.03543i) q^{95} +(0.884069 - 9.75799i) 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 $\left(\mathbb{Z}/120\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.41107	−	0.0941764i	−0.997780	−	0.0665928i
$2$	−1.41107	−	0.0941764i	−0.997780	−	0.0665928i
$3$	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
$6$	−0.429408	−	2.41156i	−0.175305	−	0.984514i
$7$	−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	$0.280843\pi$
$8$	−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	$-0.370031\pi$
$11$	2.63380			0.794119			0.397060	+	0.917793i	$0.370031\pi$
$12$	0.378815	+	3.44333i	0.109354	+	0.994003i
$13$	−3.49376	+	3.49376i	−0.968995	+	0.968995i	−0.999534	−	0.0305386i	$-0.990278\pi$
$13$	−3.49376	+	3.49376i	−0.968995	+	0.968995i	0.0305386	+	0.999534i	$0.490278\pi$
$14$	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	$0.537258\pi$
$18$	3.87551	−	1.72639i	0.913466	−	0.406914i
$19$	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	$-0.530287\pi$
$23$	4.31851	−	4.31851i	0.900472	−	0.900472i	0.995477	+	0.0950052i	$0.0302868\pi$
$24$	−0.210256	−	4.89447i	−0.0429182	−	0.999079i
$25$	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
$28$	−0.813767	+	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	$-0.145741\pi$
$30$	4.41038	+	3.24785i	0.805221	+	0.592974i
$31$	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
$33$	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
$36$	−5.63122	+	2.07108i	−0.938536	+	0.345181i
$37$	2.82150	+	2.82150i	0.463851	+	0.463851i	0.899915	−	0.436064i	$-0.143628\pi$
$37$	2.82150	+	2.82150i	0.463851	+	0.463851i	−0.436064	+	0.899915i	$0.643628\pi$
$38$	−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	$0.896257\pi$
$42$	1.02840	+	0.717517i	0.158685	+	0.110715i
$43$	7.57996	−	7.57996i	1.15593	−	1.15593i	0.170591	−	0.985342i	$-0.445432\pi$
$43$	7.57996	−	7.57996i	1.15593	−	1.15593i	0.985342	−	0.170591i	$-0.0545678\pi$
$44$	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	$0.717522\pi$
$48$	−0.164257	+	6.92626i	−0.0237085	+	0.999719i
$49$			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	$-0.230010\pi$
$53$	0.646149	+	0.646149i	0.0887554	+	0.0887554i	−0.661335	+	0.750091i	$0.730010\pi$
$54$	4.51667	+	5.79652i	0.614641	+	0.788807i
$55$	−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
$58$	−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	$0.896174\pi$
$60$	−5.91750	−	4.99832i	−0.763946	−	0.645280i
$61$		−	6.07190i		−	0.777428i	−0.921359	−	0.388714i	$-0.872919\pi$
$61$		−	6.07190i		−	0.777428i	0.921359	−	0.388714i	$-0.127081\pi$
$62$	−5.27449	−	0.352025i	−0.669861	−	0.0447072i
$63$	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
$66$	−1.13097	−	6.35155i	−0.139213	−	0.781822i
$67$	0.349085	+	0.349085i	0.0426476	+	0.0426476i	0.728109	−	0.685461i	$-0.240399\pi$
$67$	0.349085	+	0.349085i	0.0426476	+	0.0426476i	−0.685461	+	0.728109i	$0.740399\pi$
$68$	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	$0.828715\pi$
$72$	8.14111	−	2.39213i	0.959439	−	0.281915i
$73$	−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
$78$	9.92565	+	6.92516i	1.12386	+	0.784120i
$79$			4.07707i			0.458706i	0.973343	+	0.229353i	$0.0736610\pi$
$79$			4.07707i			0.458706i	−0.973343	+	0.229353i	$0.926339\pi$
$80$	−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	$-0.480611\pi$
$83$	−8.53893	−	8.53893i	−0.937270	−	0.937270i	−0.998145	+	0.0608758i	$0.980611\pi$
$84$	−1.38357	−	1.10932i	−0.150960	−	0.121037i
$85$	−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
$88$	−7.30111	−	1.47945i	−0.778301	−	0.157710i
$89$	−6.58584			−0.698097			−0.349049	−	0.937105i	$-0.613495\pi$
$89$	−6.58584			−0.698097			−0.349049	+	0.937105i	$0.613495\pi$
$90$	−3.62336	+	8.76763i	−0.381936	+	0.924189i
$91$		−	2.52941i		−	0.265154i
$92$	9.70819	−	7.41264i	1.01215	−	0.772822i
$93$	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
$96$	0.884069	−	9.75799i	0.0902299	−	0.995921i
$97$	−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	$0.265108\pi$
$98$	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	$-0.444795\pi$
$101$	3.46850			0.345129			0.172564	+	0.984998i	$0.444795\pi$
$102$	7.16228	−	10.2655i	0.709171	−	1.01644i
$103$	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	−0.841258	−	0.540634i	$-0.818184\pi$
$107$	−3.10967	+	3.10967i	−0.300623	+	0.300623i	0.540634	+	0.841258i	$0.318184\pi$
$108$	−5.82746	−	8.60469i	−0.560748	−	0.827987i
$109$	−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	$-0.655835\pi$
$113$	4.38269	−	4.38269i	0.412289	−	0.412289i	0.882535	+	0.470247i	$0.155835\pi$
$114$	−0.288676	−	1.62121i	−0.0270370	−	0.151840i
$115$	−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
$118$	0.463580	−	6.94597i	0.0426760	−	0.639428i
$119$	−2.61602			−0.239810
$120$	7.87931	+	7.61029i	0.719279	+	0.694721i
$121$	−4.06312			−0.369374
$122$	−0.571830	+	8.56791i	−0.0517711	+	0.775702i
$123$	−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
$126$	−0.777958	+	2.02783i	−0.0693060	+	0.180653i
$127$	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	$0.0369839\pi$
$128$	−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	$-0.374479\pi$
$131$	8.79462			0.768389			0.384195	+	0.923252i	$0.374479\pi$
$132$	0.997721	+	9.06902i	0.0868404	+	0.789357i
$133$	−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	$0.778656\pi$
$138$	−12.2687	−	8.55993i	−1.04438	−	0.728670i
$139$	−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
$144$	−11.7130	+	2.60877i	−0.976083	+	0.217397i
$145$	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
$148$	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	$-0.0686522\pi$
$150$	−12.1518	+	1.52799i	−0.992187	+	0.124760i
$151$	−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
$153$	−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
$156$	−13.3536	−	10.7067i	−1.06915	−	0.857220i
$157$	13.9522	+	13.9522i	1.11351	+	1.11351i	0.992673	+	0.120836i	$0.0385574\pi$
$157$	13.9522	+	13.9522i	1.11351	+	1.11351i	0.120836	+	0.992673i	$0.461443\pi$
$158$	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
$162$	−7.86397	+	10.0079i	−0.617852	+	0.786295i
$163$	6.66434	−	6.66434i	0.521992	−	0.521992i	−0.396181	−	0.918172i	$-0.629665\pi$
$163$	6.66434	−	6.66434i	0.521992	−	0.521992i	0.918172	+	0.396181i	$0.129665\pi$
$164$	−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	$-0.577111\pi$
$168$	1.84785	+	1.69563i	0.142565	+	0.130821i
$169$		−	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	$-0.138135\pi$
$173$	6.40332	+	6.40332i	0.486836	+	0.486836i	−0.420471	+	0.907306i	$0.638135\pi$
$174$	−11.4809	+	2.04433i	−0.870368	+	0.154980i
$175$	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
$178$	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	$0.993070\pi$
$180$	5.93853	−	12.0305i	0.442632	−	0.896703i
$181$		−	3.71429i		−	0.276081i	−0.990427	−	0.138040i	$-0.955920\pi$
$181$		−	3.71429i		−	0.276081i	0.990427	−	0.138040i	$-0.0440804\pi$
$182$	−0.238211	+	3.56918i	−0.0176573	+	0.264565i
$183$	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
$186$	−1.60510	−	9.01423i	−0.117691	−	0.660955i
$187$	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	$-0.301730\pi$
$192$	−2.16646	+	13.6860i	−0.156351	+	0.987702i
$193$	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	−0.758456	−	0.651724i	$-0.774046\pi$
$197$	−1.49806	+	1.49806i	−0.106733	+	0.106733i	0.651724	+	0.758456i	$0.274046\pi$
$198$	10.2073	−	4.54696i	0.725401	−	0.323138i
$199$		−	12.6160i		−	0.894328i	−0.894452	−	0.447164i	$-0.852434\pi$
$199$		−	12.6160i		−	0.894328i	0.894452	−	0.447164i	$-0.147566\pi$
$200$	−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
$204$	−11.0733	+	13.8109i	−0.775284	+	0.966955i
$205$	−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
$208$	−17.1628	+	9.80011i	−1.19003	+	0.679515i
$209$	1.77061			0.122476
$210$	−2.77220	+	0.420822i	−0.191300	+	0.0290395i
$211$		−	14.0010i		−	0.963865i	−0.876208	−	0.481933i	$-0.839935\pi$
$211$		−	14.0010i		−	0.963865i	0.876208	−	0.481933i	$-0.160065\pi$
$212$	1.10910	+	1.45257i	0.0761736	+	0.0997630i
$213$	−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
$216$	7.41263	+	12.6907i	0.504365	+	0.863490i
$217$	−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
$222$	5.59263	−	8.01577i	0.375352	−	0.537983i
$223$	−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	−0.107205	−	0.994237i	$-0.534190\pi$
$227$	13.3645	−	13.3645i	0.887032	−	0.887032i	0.994237	+	0.107205i	$0.0341901\pi$
$228$	0.254664	+	2.31483i	0.0168655	+	0.153303i
$229$	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	$-0.956079\pi$
$233$	−13.0197	+	13.0197i	−0.852949	+	0.852949i	0.137546	+	0.990495i	$0.456079\pi$
$234$	−7.50851	+	19.5717i	−0.490847	+	1.27944i
$235$	−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
$238$	3.69139	+	0.246367i	0.239278	+	0.0159696i
$239$	24.8336			1.60635			0.803177	−	0.595740i	$-0.203141\pi$
$239$	24.8336			1.60635			0.803177	+	0.595740i	$0.203141\pi$
$240$	−10.4016	−	11.4807i	−0.671419	−	0.741078i
$241$	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
$243$	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
$246$	9.88804	−	1.76069i	0.630438	−	0.112257i
$247$	−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	$-0.489447\pi$
$251$	1.05032			0.0662958			0.0331479	+	0.999450i	$0.489447\pi$
$252$	1.28873	−	2.78815i	0.0811824	−	0.175637i
$253$	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	$0.719019\pi$
$258$	−21.5344	−	15.0246i	−1.34067	−	0.935392i
$259$	−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	$-0.643966\pi$
$263$	7.49936	−	7.49936i	0.462430	−	0.462430i	0.899451	+	0.437021i	$0.143966\pi$
$264$	−0.553770	−	12.8910i	−0.0340822	−	0.793388i
$265$	−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
$268$	0.599199	+	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	$-0.223673\pi$
$270$	−16.2495	−	2.43979i	−0.988915	−	0.148481i
$271$	−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
$273$	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
$276$	16.5060	+	13.2341i	0.993542	+	0.796601i
$277$	−8.79593	−	8.79593i	−0.528496	−	0.528496i	0.391628	−	0.920124i	$-0.371912\pi$
$277$	−8.79593	−	8.79593i	−0.528496	−	0.528496i	−0.920124	+	0.391628i	$0.871912\pi$
$278$	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	$-0.00466021\pi$
$282$	1.95745	−	2.80556i	0.116564	−	0.167069i
$283$	−9.43710	+	9.43710i	−0.560978	+	0.560978i	−0.929585	−	0.368608i	$-0.879835\pi$
$283$	−9.43710	+	9.43710i	−0.560978	+	0.560978i	0.368608	+	0.929585i	$0.379835\pi$
$284$	−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
$288$	16.7736	−	2.57807i	0.988394	−	0.151914i
$289$			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	$-0.196985\pi$
$293$	4.01316	+	4.01316i	0.234451	+	0.234451i	−0.580096	+	0.814548i	$0.696985\pi$
$294$	16.2489	−	2.89332i	0.947655	−	0.168742i
$295$	−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
$298$	−0.492036	+	7.37233i	−0.0285029	+	0.427068i
$299$			30.1757i			1.74510i
$300$	17.2909	−	1.01170i	0.998293	−	0.0584103i
$301$			5.48773i			0.316307i
$302$	16.7228	+	1.11609i	0.962288	+	0.0642240i
$303$	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
$306$	20.2418	+	7.76561i	1.15715	+	0.443930i
$307$	−8.00887	−	8.00887i	−0.457091	−	0.457091i	0.440609	−	0.897699i	$-0.354763\pi$
$307$	−8.00887	−	8.00887i	−0.457091	−	0.457091i	−0.897699	+	0.440609i	$0.854763\pi$
$308$	−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	$-0.119064\pi$
$312$	17.8347	+	16.3655i	1.00969	+	0.926515i
$313$	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	−0.917290	−	0.398221i	$-0.869628\pi$
$317$	−9.24176	+	9.24176i	−0.519069	+	0.519069i	0.398221	+	0.917290i	$0.369628\pi$
$318$	1.28076	−	1.83569i	0.0718217	−	0.102940i
$319$		−	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
$324$	12.0392	−	13.3813i	0.668842	−	0.743405i
$325$	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
$328$	2.30319	−	11.3663i	0.127173	−	0.627600i
$329$	−0.714956			−0.0394168
$330$	11.6160	+	8.55418i	0.639442	+	0.470892i
$331$			22.2355i			1.22218i	0.791563	+	0.611088i	$0.209268\pi$
$331$			22.2355i			1.22218i	−0.791563	+	0.611088i	$0.790732\pi$
$332$	−14.6569	−	19.1959i	−0.804403	−	1.05351i
$333$	−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
$336$	−2.44777	−	2.56669i	−0.133537	−	0.140024i
$337$	−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	$0.362516\pi$
$338$	−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
$342$	2.60537	−	1.16059i	0.140882	−	0.0627577i
$343$	−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	−0.910450	−	0.413619i	$-0.864265\pi$
$347$	−9.25494	+	9.25494i	−0.496831	+	0.496831i	0.413619	+	0.910450i	$0.364265\pi$
$348$	16.3930	−	1.80346i	0.878756	−	0.0966756i
$349$	−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	$-0.587742\pi$
$353$	12.9654	−	12.9654i	0.690077	−	0.690077i	0.962249	+	0.272172i	$0.0877419\pi$
$354$	11.8708	−	2.11375i	0.630927	−	0.112344i
$355$	−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
$358$	0.0548601	−	0.821985i	0.00289945	−	0.0434433i
$359$	16.5244			0.872125			0.436063	−	0.899916i	$-0.356373\pi$
$359$	16.5244			0.872125			0.436063	+	0.899916i	$0.356373\pi$
$360$	−9.51270	+	16.4167i	−0.501364	+	0.865237i
$361$	−18.5481			−0.976214
$362$	−0.349798	+	5.24113i	−0.0183850	+	0.275468i
$363$	−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
$366$	−14.6427	+	2.60732i	−0.765389	+	0.136287i
$367$	−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	$0.890660\pi$
$368$	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
$372$	1.41598	+	12.8709i	0.0734152	+	0.667325i
$373$	−0.406084	+	0.406084i	−0.0210262	+	0.0210262i	−0.717542	−	0.696516i	$-0.754733\pi$
$373$	−0.406084	+	0.406084i	−0.0210262	+	0.0210262i	0.696516	+	0.717542i	$0.254733\pi$
$374$	−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
$378$	−3.73327	−	0.463292i	−0.192018	−	0.0238292i
$379$	−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	$-0.964346\pi$
$383$	−17.2603	+	17.2603i	−0.881958	+	0.881958i	0.111775	+	0.993734i	$0.464346\pi$
$384$	4.34593	−	19.1079i	0.221777	−	0.975097i
$385$	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
$388$	−1.48564	+	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	$0.749574\pi$
$390$	−26.7560	+	4.06159i	−1.35484	+	0.205666i
$391$	31.2089			1.57830
$392$	3.78481	−	18.6781i	0.191162	−	0.943388i
$393$	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
$396$	−14.8315	+	5.45481i	−0.745310	+	0.274115i
$397$	−3.16232	−	3.16232i	−0.158712	−	0.158712i	0.623284	−	0.781996i	$-0.285798\pi$
$397$	−3.16232	−	3.16232i	−0.158712	−	0.158712i	−0.781996	+	0.623284i	$0.785798\pi$
$398$	−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	$-0.0906578\pi$
$402$	0.691940	−	0.991740i	0.0345108	−	0.0494635i
$403$	−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
$408$	16.9259	−	18.4453i	0.837956	−	0.913181i
$409$			5.05965i			0.250183i	0.992145	+	0.125092i	$0.0399225\pi$
$409$			5.05965i			0.250183i	−0.992145	+	0.125092i	$0.960077\pi$
$410$	8.28533	+	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
$414$	9.28099	−	24.1919i	0.456136	−	1.18897i
$415$	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
$418$	−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	$-0.210891\pi$
$420$	3.95141	−	0.332735i	0.192809	−	0.0162358i
$421$		−	31.5091i		−	1.53566i	−0.640654	−	0.767830i	$-0.721336\pi$
$421$		−	31.5091i		−	1.53566i	0.640654	−	0.767830i	$-0.278664\pi$
$422$	−1.31856	+	19.7564i	−0.0641865	+	0.961726i
$423$	−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
$426$	20.8287	−	3.70880i	1.00915	−	0.179692i
$427$	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	$0.893713\pi$
$432$	−9.26461	−	18.6056i	−0.445744	−	0.895161i
$433$	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
$438$	−22.4500	+	32.1770i	−1.07270	+	1.53748i
$439$			5.56599i			0.265650i	0.991139	+	0.132825i	$0.0424049\pi$
$439$			5.56599i			0.265650i	−0.991139	+	0.132825i	$0.957595\pi$
$440$	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	$-0.212113\pi$
$443$	3.53450	+	3.53450i	0.167929	+	0.167929i	−0.618139	+	0.786069i	$0.712113\pi$
$444$	−8.64651	+	10.7842i	−0.410345	+	0.511793i
$445$	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
$448$	−3.79481	+	1.54015i	−0.179288	+	0.0727653i
$449$	−21.1895			−0.999995			−0.499998	−	0.866027i	$-0.666666\pi$
$449$	−21.1895			−0.999995			−0.499998	+	0.866027i	$0.666666\pi$
$450$	−7.63033	−	19.7934i	−0.359697	−	0.933069i
$451$			10.7993i			0.508518i
$452$	9.85246	−	7.52280i	0.463421	−	0.353843i
$453$	−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
$456$	−0.141348	−	3.29038i	−0.00661921	−	0.154086i
$457$	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	$0.0614509\pi$
$458$	−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	$-0.526634\pi$
$461$	−3.58886			−0.167150			−0.0835749	+	0.996502i	$0.526634\pi$
$462$	2.70859	+	1.88979i	0.126015	+	0.0879211i
$463$	−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	−0.0195348	−	0.999809i	$-0.506219\pi$
$467$	21.1839	−	21.1839i	0.980274	−	0.980274i	0.999809	+	0.0195348i	$0.00621850\pi$
$468$	12.4383	−	26.9100i	0.574959	−	1.24392i
$469$	−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
$474$	9.83208	−	1.75073i	0.451603	−	0.0804135i
$475$	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
$478$	−35.0421	−	2.33874i	−1.60279	−	0.106972i
$479$	−2.58847			−0.118270			−0.0591350	−	0.998250i	$-0.518834\pi$
$479$	−2.58847			−0.118270			−0.0591350	+	0.998250i	$0.518834\pi$
$480$	13.5962	+	17.1797i	0.620579	+	0.784144i
$481$	−19.7153			−0.898939
$482$	−24.4103	−	1.62916i	−1.11186	−	0.0742063i
$483$	−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
$486$	−20.1010	−	9.05261i	−0.911800	−	0.410635i
$487$	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	$0.164317\pi$
$488$	−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	$-0.694015\pi$
$491$	−25.3703			−1.14494			−0.572472	+	0.819924i	$0.694015\pi$
$492$	−14.1186	+	1.55324i	−0.636514	+	0.0700256i
$493$	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
$498$	−16.9254	+	24.2588i	−0.758447	+	1.08706i
$499$	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	$-0.805171\pi$
$503$	−5.46994	+	5.46994i	−0.243893	+	0.243893i	0.574566	+	0.818458i	$0.305171\pi$
$504$	−2.08107	+	3.81292i	−0.0926983	+	0.169841i
$505$	−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
$508$	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	$-0.159473\pi$
$510$	4.20066	+	27.6722i	0.186008	+	1.22534i
$511$	8.19983			0.362739
$512$	−18.6780	−	12.7723i	−0.825460	−	0.564460i
$513$	−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
$516$	28.9717	+	23.2289i	1.27541	+	1.02259i
$517$	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	$0.907911\pi$
$522$	−8.21900	−	18.4505i	−0.359736	−	0.807558i
$523$	−1.57962	+	1.57962i	−0.0690720	+	0.0690720i	−0.740799	−	0.671727i	$-0.765553\pi$
$523$	−1.57962	+	1.57962i	−0.0690720	+	0.0690720i	0.671727	+	0.740799i	$0.265553\pi$
$524$	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
$528$	−0.432619	+	18.2423i	−0.0188273	+	0.793896i
$529$		−	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
$534$	2.82801	+	15.8821i	0.122380	+	0.687287i
$535$	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
$538$	−1.99647	+	29.9137i	−0.0860740	+	1.28967i
$539$			17.7463i			0.764388i
$540$	22.6995	+	4.97305i	0.976832	+	0.214006i
$541$			38.6062i			1.65981i	0.557903	+	0.829906i	$0.311606\pi$
$541$			38.6062i			1.65981i	−0.557903	+	0.829906i	$0.688394\pi$
$542$	20.7072	+	1.38202i	0.889452	+	0.0593629i
$543$	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
$546$	−6.09981	+	1.08615i	−0.261048	+	0.0464828i
$547$	16.8276	+	16.8276i	0.719498	+	0.719498i	0.968502	−	0.249005i	$-0.0801034\pi$
$547$	16.8276	+	16.8276i	0.719498	+	0.719498i	−0.249005	+	0.968502i	$0.580103\pi$
$548$	−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
$552$	−22.0448	−	20.2288i	−0.938288	−	0.860995i
$553$	−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	−0.959020	−	0.283337i	$-0.908559\pi$
$557$	−15.9467	+	15.9467i	−0.675684	+	0.675684i	0.283337	+	0.959020i	$0.408559\pi$
$558$	14.4864	−	6.45312i	0.613257	−	0.273182i
$559$			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	$-0.228360\pi$
$563$	2.27954	+	2.27954i	0.0960712	+	0.0960712i	−0.657438	+	0.753509i	$0.728360\pi$
$564$	−3.02632	+	3.77451i	−0.127431	+	0.158935i
$565$	−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
$568$	4.85156	−	23.9426i	0.203567	−	1.00461i
$569$	−38.0835			−1.59654			−0.798272	−	0.602297i	$-0.794252\pi$
$569$	−38.0835			−1.59654			−0.798272	+	0.602297i	$0.794252\pi$
$570$	2.96495	+	2.18342i	0.124188	+	0.0914534i
$571$		−	39.4382i		−	1.65044i	−0.564815	−	0.825218i	$-0.691052\pi$
$571$		−	39.4382i		−	1.65044i	0.564815	−	0.825218i	$-0.308948\pi$
$572$	−20.6861	+	15.7948i	−0.864931	+	0.660414i
$573$	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
$576$	−23.9116	+	2.05818i	−0.996316	+	0.0857574i
$577$	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	$0.0974770\pi$
$578$	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
$582$	1.87748	+	1.30992i	0.0778240	+	0.0542980i
$583$	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	−0.521600	−	0.853190i	$-0.674665\pi$
$587$	8.03380	−	8.03380i	0.331590	−	0.331590i	0.853190	+	0.521600i	$0.174665\pi$
$588$	−23.2009	+	2.55243i	−0.956788	+	0.105260i
$589$	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	$-0.900779\pi$
$593$	−15.7097	+	15.7097i	−0.645122	+	0.645122i	0.306688	+	0.951810i	$0.400779\pi$
$594$	11.8960	+	15.2669i	0.488098	+	0.626407i
$595$	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
$598$	2.84184	−	42.5801i	0.116211	−	1.74123i
$599$	−16.2242			−0.662902			−0.331451	−	0.943473i	$-0.607538\pi$
$599$	−16.2242			−0.662902			−0.331451	+	0.943473i	$0.607538\pi$
$600$	−24.4941	−	0.200819i	−0.999966	−	0.00819841i
$601$	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
$603$	−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
$606$	−1.48940	−	8.36449i	−0.0605028	−	0.339784i
$607$	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	$-0.0276208\pi$
$608$	−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
$612$	−27.8314	−	12.8642i	−1.12502	−	0.520003i
$613$	−11.2416	+	11.2416i	−0.454046	+	0.454046i	−0.896695	−	0.442649i	$-0.854039\pi$
$613$	−11.2416	+	11.2416i	−0.454046	+	0.454046i	0.442649	+	0.896695i	$0.354039\pi$
$614$	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	$0.898905\pi$
$618$	17.2210	−	24.6825i	0.692732	−	0.992875i
$619$	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
$624$	−23.6248	−	24.7726i	−0.945749	−	0.991696i
$625$	−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
$628$	23.9487	+	31.3652i	0.955658	+	1.25161i
$629$			20.3903i			0.813016i
$630$	−1.86217	−	4.48540i	−0.0741906	−	0.178703i
$631$	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
$633$	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
$636$	−1.98013	+	2.46967i	−0.0785174	+	0.0979290i
$637$	−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	$0.685733\pi$
$642$	8.83447	+	6.16383i	0.348669	+	0.243267i
$643$	−15.1060	+	15.1060i	−0.595722	+	0.595722i	−0.939171	−	0.343449i	$-0.888405\pi$
$643$	−15.1060	+	15.1060i	−0.595722	+	0.595722i	0.343449	+	0.939171i	$0.388405\pi$
$644$	−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	$0.849933\pi$
$648$	−18.2483	+	17.7482i	−0.716863	+	0.697215i
$649$			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	$-0.109218\pi$
$653$	15.4673	+	15.4673i	0.605283	+	0.605283i	−0.336426	+	0.941710i	$0.609218\pi$
$654$	1.77912	+	9.99156i	0.0695692	+	0.390701i
$655$	−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
$658$	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	$-0.0368641\pi$
$660$	−15.5855	−	13.1645i	−0.606664	−	0.512429i
$661$			28.1054i			1.09317i	0.837403	+	0.546586i	$0.184073\pi$
$661$			28.1054i			1.09317i	−0.837403	+	0.546586i	$0.815927\pi$
$662$	2.09406	−	31.3760i	0.0813881	−	1.21946i
$663$	−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
$666$	15.8057	+	6.06373i	0.612460	+	0.234965i
$667$	−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
$672$	3.21227	+	3.85231i	0.123916	+	0.148606i
$673$	−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	$-0.471620\pi$
$677$	28.2327	−	28.2327i	1.08507	−	1.08507i	0.996028	−	0.0890415i	$-0.0283804\pi$
$678$	−12.4511	−	8.68714i	−0.478180	−	0.333628i
$679$		−	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	$-0.000319371\pi$
$683$	26.1080	+	26.1080i	0.998996	+	0.998996i	−0.00100333	+	0.999999i	$0.500319\pi$
$684$	−3.78567	+	1.39232i	−0.144749	+	0.0532366i
$685$	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
$688$	37.2359	−	21.2620i	1.41961	−	0.810607i
$689$	−4.51498			−0.172007
$690$	33.0722	−	5.02038i	1.25904	−	0.191123i
$691$			9.65683i			0.367363i	0.982986	+	0.183682i	$0.0588015\pi$
$691$			9.65683i			0.367363i	−0.982986	+	0.183682i	$0.941198\pi$
$692$	10.9912	+	14.3949i	0.417822	+	0.547213i
$693$	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
$696$	−23.3016	+	1.00098i	−0.883244	+	0.0379422i
$697$	−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	$-0.638041\pi$
$701$	−22.2509			−0.840403			−0.420202	+	0.907431i	$0.638041\pi$
$702$	−36.0318	−	4.47149i	−1.35993	−	0.168766i
$703$	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
$708$	−16.9497	+	1.86470i	−0.637008	+	0.0700799i
$709$	−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
$714$	1.12334	+	6.30867i	0.0420399	+	0.236096i
$715$	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
$718$	−23.3172	−	1.55621i	−0.870189	−	0.0580772i
$719$	4.65932			0.173763			0.0868817	−	0.996219i	$-0.472310\pi$
$719$	4.65932			0.173763			0.0868817	+	0.996219i	$0.472310\pi$
$720$	14.9692	−	22.2693i	0.557869	−	0.829929i
$721$	−6.28997			−0.234251
$722$	26.1727	+	1.74679i	0.974047	+	0.0650088i
$723$	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
$726$	1.74474	+	9.79845i	0.0647532	+	0.363654i
$727$	−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	$0.976856\pi$
$728$	−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
$732$	20.9075	−	2.30013i	0.772765	−	0.0850151i
$733$	−23.8359	+	23.8359i	−0.880398	+	0.880398i	−0.993575	−	0.113177i	$-0.963897\pi$
$733$	−23.8359	+	23.8359i	−0.880398	+	0.880398i	0.113177	+	0.993575i	$0.463897\pi$
$734$	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
$738$	7.07867	+	15.8906i	0.260569	+	0.584943i
$739$	−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	$-0.820082\pi$
$743$	−8.41878	+	8.41878i	−0.308855	+	0.308855i	0.535610	+	0.844465i	$0.320082\pi$
$744$	−0.785920	−	18.2952i	−0.0288132	−	0.670733i
$745$	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
$748$	16.3356	+	21.3945i	0.597290	+	0.782259i
$749$		−	2.25134i		−	0.0822620i
$750$	17.3451	−	21.1931i	0.633352	−	0.773864i
$751$	−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
$753$	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
$756$	5.22428	+	1.00533i	0.190005	+	0.0365633i
$757$	−25.5118	−	25.5118i	−0.927244	−	0.927244i	0.0702832	−	0.997527i	$-0.477610\pi$
$757$	−25.5118	−	25.5118i	−0.927244	−	0.927244i	−0.997527	+	0.0702832i	$0.977610\pi$
$758$	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	$0.986710\pi$
$762$	−28.0887	−	19.5975i	−1.01754	−	0.709944i
$763$	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
$768$	−7.93195	+	26.5534i	−0.286220	+	0.958164i
$769$		−	46.5571i		−	1.67889i	−0.543442	−	0.839447i	$-0.682879\pi$
$769$		−	46.5571i		−	1.67889i	0.543442	−	0.839447i	$-0.317121\pi$
$770$	−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	$-0.412857\pi$
$773$	−19.2506	−	19.2506i	−0.692397	−	0.692397i	−0.962759	+	0.270362i	$0.912857\pi$
$774$	16.2902	−	42.4622i	0.585541	−	1.52627i
$775$	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
$778$	2.63035	−	39.4113i	0.0943024	−	1.41296i
$779$			2.75647i			0.0987608i
$780$	38.1373	−	3.21141i	1.36553	−	0.114987i
$781$			22.7481i			0.813993i
$782$	−44.0381	−	2.93914i	−1.57480	−	0.105104i
$783$	−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
$786$	−3.77648	−	21.2087i	−0.134702	−	0.756490i
$787$	−3.79411	−	3.79411i	−0.135246	−	0.135246i	0.636243	−	0.771489i	$-0.280488\pi$
$787$	−3.79411	−	3.79411i	−0.135246	−	0.135246i	−0.771489	+	0.636243i	$0.780488\pi$
$788$	−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
$792$	21.4420	−	6.30037i	0.761909	−	0.223874i
$793$	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	$0.521530\pi$
$797$	−30.0747	+	30.0747i	−1.06530	+	1.06530i	−0.997713	+	0.0675880i	$0.978470\pi$
$798$	0.691357	+	0.482362i	0.0244738	+	0.0170754i
$799$			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
$804$	−1.06978	+	1.33425i	−0.0377281	+	0.0470555i
$805$	−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
$808$	−9.61499	−	1.94832i	−0.338254	−	0.0685416i
$809$	21.7890			0.766061			0.383031	−	0.923736i	$-0.374880\pi$
$809$	21.7890			0.766061			0.383031	+	0.923736i	$0.374880\pi$
$810$	−2.66641	−	28.3353i	−0.0936880	−	0.995602i
$811$		−	2.48698i		−	0.0873295i	−0.999046	−	0.0436648i	$-0.986097\pi$
$811$		−	2.48698i		−	0.0873295i	0.999046	−	0.0436648i	$-0.0139033\pi$
$812$	2.95811	+	3.87418i	0.103809	+	0.135957i
$813$	−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
$816$	−25.6208	+	24.4337i	−0.896907	+	0.855352i
$817$	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	$-0.458173\pi$
$821$	7.50855			0.262050			0.131025	+	0.991379i	$0.458173\pi$
$822$	−2.94982	+	4.22791i	−0.102887	+	0.147465i
$823$	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	−0.967985	−	0.251007i	$-0.919238\pi$
$827$	−20.6186	+	20.6186i	−0.716979	+	0.716979i	0.251007	+	0.967985i	$0.419238\pi$
$828$	−15.3745	+	33.2625i	−0.534300	+	1.15595i
$829$	−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
$834$	5.71232	+	32.0804i	0.197801	+	1.11085i
$835$	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
$838$	−2.37157	+	35.5340i	−0.0819246	+	1.22750i
$839$	−31.3869			−1.08360			−0.541798	−	0.840509i	$-0.682256\pi$
$839$	−31.3869			−1.08360			−0.541798	+	0.840509i	$0.682256\pi$
$840$	−5.60707	+	0.0973847i	−0.193462	+	0.00336009i
$841$	6.33479			0.218441
$842$	−2.96742	+	44.4617i	−0.102264	+	1.53225i
$843$	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
$846$	5.53209	+	2.12234i	0.190197	+	0.0729674i
$847$	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
$852$	−29.7401	+	3.27183i	−1.01888	+	0.112091i
$853$	4.93576	−	4.93576i	0.168997	−	0.168997i	−0.617541	−	0.786538i	$-0.711871\pi$
$853$	4.93576	−	4.93576i	0.168997	−	0.168997i	0.786538	+	0.617541i	$0.211871\pi$
$854$	−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	$0.553940\pi$
$858$	26.1421	+	18.2394i	0.892478	+	0.622685i
$859$	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	0.354918	−	0.934897i	$-0.384509\pi$
$863$	37.8907	−	37.8907i	1.28982	−	1.28982i	0.934897	−	0.354918i	$-0.115491\pi$
$864$	11.3208	+	27.1263i	0.385143	+	0.922857i
$865$	−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
$868$	−3.04180	+	2.32255i	−0.103245	+	0.0788326i
$869$			10.7382i			0.364267i
$870$	15.4624	−	20.9969i	0.524224	−	0.711863i
$871$	−2.43924			−0.0826506
$872$	11.4853	+	2.32731i	0.388942	+	0.0788125i
$873$	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
$876$	34.7089	−	43.2899i	1.17270	−	1.46263i
$877$	19.4977	+	19.4977i	0.658392	+	0.658392i	0.954999	−	0.296608i	$-0.0958553\pi$
$877$	19.4977	+	19.4977i	0.658392	+	0.658392i	−0.296608	+	0.954999i	$0.595855\pi$
$878$	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	$-0.213166\pi$
$882$	11.6323	+	26.1129i	0.391680	+	0.879267i
$883$	25.6982	−	25.6982i	0.864813	−	0.864813i	−0.127079	−	0.991893i	$-0.540560\pi$
$883$	25.6982	−	25.6982i	0.864813	−	0.864813i	0.991893	+	0.127079i	$0.0405602\pi$
$884$	−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	$0.598171\pi$
$888$	13.2165	−	14.4029i	0.443516	−	0.483331i
$889$			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
$894$	−12.5995	+	2.24349i	−0.421390	+	0.0750337i
$895$	−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
$898$	29.9000	+	1.99555i	0.997775	+	0.0665925i
$899$		−	17.7955i		−	0.593514i
$900$	8.90289	+	28.6485i	0.296763	+	0.954951i
$901$			4.66958i			0.155566i
$902$	1.01704	−	15.2386i	0.0338636	−	0.507389i
$903$	−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
$906$	5.08896	+	28.5796i	0.169069	+	0.949494i
$907$	−16.8535	−	16.8535i	−0.559613	−	0.559613i	0.369585	−	0.929197i	$-0.379500\pi$
$907$	−16.8535	−	16.8535i	−0.559613	−	0.559613i	−0.929197	+	0.369585i	$0.879500\pi$
$908$	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	$0.825872\pi$
$912$	−0.110424	+	4.65628i	−0.00365652	+	0.154185i
$913$	−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
$918$	−4.62460	+	37.2656i	−0.152635	+	1.22995i
$919$		−	26.0422i		−	0.859054i	−0.903054	−	0.429527i	$-0.858680\pi$
$919$		−	26.0422i		−	0.859054i	0.903054	−	0.429527i	$-0.141320\pi$
$920$	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
$924$	−3.64405	−	2.92172i	−0.119881	−	0.0961177i
$925$	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
$928$	−8.80860	+	25.4499i	−0.289157	+	0.835433i
$929$	16.2184			0.532108			0.266054	−	0.963958i	$-0.414280\pi$
$929$	16.2184			0.532108			0.266054	+	0.963958i	$0.414280\pi$
$930$	16.4857	+	12.1402i	0.540587	+	0.398094i
$931$			4.52968i			0.148454i
$932$	−29.2688	+	22.3481i	−0.958733	+	0.732036i
$933$	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
$936$	−20.0856	+	36.8006i	−0.656518	+	1.20287i
$937$	−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	$0.357611\pi$
$938$	0.356621	+	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	$-0.353059\pi$
$941$	27.3264			0.890817			0.445408	+	0.895328i	$0.353059\pi$
$942$	27.6554	−	39.6378i	0.901061	−	1.29147i
$943$	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	−0.932063	−	0.362297i	$-0.881993\pi$
$947$	−17.5336	+	17.5336i	−0.569766	+	0.569766i	0.362297	+	0.932063i	$0.381993\pi$
$948$	−14.0387	+	1.54445i	−0.455955	+	0.0501615i
$949$	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	$-0.601915\pi$
$953$	19.5859	−	19.5859i	0.634449	−	0.634449i	0.949181	+	0.314732i	$0.101915\pi$
$954$	3.61966	+	1.38865i	0.117191	+	0.0449593i
$955$	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
$958$	3.65252	+	0.243772i	0.118008	+	0.00787593i
$959$	1.07742			0.0347917
$960$	−17.5673	−	25.5223i	−0.566983	−	0.823730i
$961$	−17.0279			−0.549287
$962$	27.8197	+	1.85671i	0.896943	+	0.0598628i
$963$	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
$966$	7.53975	−	1.34255i	0.242588	−	0.0431958i
$967$	−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	$0.369242\pi$
$968$	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	$-0.856995\pi$
$971$	−56.1374			−1.80154			−0.900768	+	0.434301i	$0.856995\pi$
$972$	27.5115	+	14.6669i	0.882431	+	0.470442i
$973$	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	$0.760860\pi$
$978$	−18.9332	−	13.2097i	−0.605416	−	0.422400i
$979$	−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	$-0.900248\pi$
$983$	−20.1605	+	20.1605i	−0.643021	+	0.643021i	0.308276	+	0.951297i	$0.400248\pi$
$984$	20.0686	−	0.862105i	0.639765	−	0.0274829i
$985$	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
$988$	−5.28006	+	4.03156i	−0.167981	+	0.128261i
$989$		−	65.4683i		−	2.08177i
$990$	−9.54319	+	23.0921i	−0.303302	+	0.733916i
$991$	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
$993$	−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
$996$	26.1677	−	32.6370i	0.829154	−	1.03414i
$997$	−28.1250	−	28.1250i	−0.890726	−	0.890726i	0.103865	−	0.994591i	$-0.466879\pi$
$997$	−28.1250	−	28.1250i	−0.890726	−	0.890726i	−0.994591	+	0.103865i	$0.966879\pi$
$998$	−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.53.1	✓	32
3.2	odd	2	inner	120.2.w.c.53.16	yes	32
4.3	odd	2		480.2.bi.c.113.7		32
5.2	odd	4	inner	120.2.w.c.77.9	yes	32
5.3	odd	4		600.2.w.j.557.8		32
5.4	even	2		600.2.w.j.293.16		32
8.3	odd	2		480.2.bi.c.113.10		32
8.5	even	2	inner	120.2.w.c.53.8	yes	32
12.11	even	2		480.2.bi.c.113.15		32
15.2	even	4	inner	120.2.w.c.77.8	yes	32
15.8	even	4		600.2.w.j.557.9		32
15.14	odd	2		600.2.w.j.293.1		32
20.7	even	4		480.2.bi.c.17.2		32
24.5	odd	2	inner	120.2.w.c.53.9	yes	32
24.11	even	2		480.2.bi.c.113.2		32
40.13	odd	4		600.2.w.j.557.1		32
40.27	even	4		480.2.bi.c.17.15		32
40.29	even	2		600.2.w.j.293.9		32
40.37	odd	4	inner	120.2.w.c.77.16	yes	32
60.47	odd	4		480.2.bi.c.17.10		32
120.29	odd	2		600.2.w.j.293.8		32
120.53	even	4		600.2.w.j.557.16		32
120.77	even	4	inner	120.2.w.c.77.1	yes	32
120.107	odd	4		480.2.bi.c.17.7		32

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

\(f(q)\)	\(=\)	\(q+(-1.41107 - 0.0941764i) q^{2} +(0.416519 + 1.68122i) q^{3} +(1.98226 + 0.265780i) q^{4} +(-1.62104 + 1.54020i) q^{5} +(-0.429408 - 2.41156i) q^{6} +(-0.361989 + 0.361989i) q^{7} +(-2.77209 - 0.561717i) q^{8} +(-2.65302 + 1.40052i) q^{9} +O(q^{10})\)	\(q+(-1.41107 - 0.0941764i) q^{2} +(0.416519 + 1.68122i) q^{3} +(1.98226 + 0.265780i) q^{4} +(-1.62104 + 1.54020i) q^{5} +(-0.429408 - 2.41156i) 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} +(0.378815 + 3.44333i) 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} +(3.87551 - 1.72639i) 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} +(-0.210256 - 4.89447i) q^{24} +(0.255538 - 4.99347i) q^{25} +(5.25899 - 4.60093i) q^{26} +(-3.45963 - 3.87698i) q^{27} +(-0.813767 + 0.621348i) q^{28} -4.76080i q^{29} +(4.41038 + 3.24785i) q^{30} +3.73793 q^{31} +(-5.34571 - 1.85024i) q^{32} +(1.09703 + 4.42800i) q^{33} +(-4.75847 - 5.43906i) q^{34} +(0.0292613 - 1.14434i) q^{35} +(-5.63122 + 2.07108i) 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} +(1.02840 + 0.717517i) 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} +(-0.164257 + 6.92626i) 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} +(4.51667 + 5.79652i) q^{54} +(-4.26949 + 4.05659i) q^{55} +(1.20680 - 0.800131i) q^{56} +(0.280012 + 1.13023i) q^{57} +(-0.448355 + 6.71784i) q^{58} +4.92247i q^{59} +(-5.91750 - 4.99832i) q^{60} -6.07190i q^{61} +(-5.27449 - 0.352025i) q^{62} +(0.453392 - 1.46734i) q^{63} +(7.36895 + 3.11426i) q^{64} +(0.282417 - 11.0446i) q^{65} +(-1.13097 - 6.35155i) 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} +(8.14111 - 2.39213i) 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} +(9.92565 + 6.92516i) 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} +(-1.38357 - 1.10932i) q^{84} +(-11.4228 - 0.292087i) q^{85} +(-11.4097 + 9.98203i) q^{86} +(8.00397 - 1.98296i) q^{87} +(-7.30111 - 1.47945i) q^{88} -6.58584 q^{89} +(-3.62336 + 8.76763i) q^{90} -2.52941i q^{91} +(9.70819 - 7.41264i) q^{92} +(1.55692 + 6.28429i) q^{93} +(-1.30049 - 1.48649i) q^{94} +(-1.08977 + 1.03543i) q^{95} +(0.884069 - 9.75799i) 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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