LMFDB - Embedded newform 1254.2.k.b.373.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1254,2,Mod(373,1254)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1254, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1254.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1254 = 2 \cdot 3 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1254.k (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.0132404135$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			373.1
Character	$\chi$	$=$	1254.373
Dual form			1254.2.k.b.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.72386 + 2.98582i) q^{5} +(-0.866025 - 0.500000i) q^{6} +1.24837i q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.72386 + 2.98582i) q^{10} +(1.18259 + 3.09863i) q^{11} -1.00000i q^{12} +(-0.821877 + 1.42353i) q^{13} +(-1.08112 + 0.624183i) q^{14} +(-2.98582 - 1.72386i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.951116 + 0.549127i) q^{17} +1.00000 q^{18} +(2.90459 + 3.25014i) q^{19} -3.44773 q^{20} +(-0.624183 - 1.08112i) q^{21} +(-2.09220 + 2.57346i) q^{22} +(3.42976 - 5.94051i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-3.44340 + 5.96415i) q^{25} -1.64375 q^{26} +1.00000i q^{27} +(-1.08112 - 0.624183i) q^{28} +(-0.766066 + 1.32687i) q^{29} -3.44773i q^{30} -2.62142i q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.57346 - 2.09220i) q^{33} +(-0.951116 - 0.549127i) q^{34} +(-3.72739 + 2.15201i) q^{35} +(0.500000 + 0.866025i) q^{36} +2.80047i q^{37} +(-1.36241 + 4.14051i) q^{38} -1.64375i q^{39} +(-1.72386 - 2.98582i) q^{40} +(-2.04813 - 3.54746i) q^{41} +(0.624183 - 1.08112i) q^{42} +(-1.73718 + 1.00296i) q^{43} +(-3.27478 - 0.525163i) q^{44} +3.44773 q^{45} +6.85951 q^{46} +(0.386049 - 0.668656i) q^{47} +(0.866025 + 0.500000i) q^{48} +5.44158 q^{49} -6.88681 q^{50} +(0.549127 - 0.951116i) q^{51} +(-0.821877 - 1.42353i) q^{52} +(-7.64033 - 4.41114i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-7.21332 + 8.87260i) q^{55} -1.24837i q^{56} +(-4.14051 - 1.36241i) q^{57} -1.53213 q^{58} +(7.93429 - 4.58086i) q^{59} +(2.98582 - 1.72386i) q^{60} +(-4.04837 - 2.33733i) q^{61} +(2.27022 - 1.31071i) q^{62} +(1.08112 + 0.624183i) q^{63} +1.00000 q^{64} -5.66721 q^{65} +(0.525163 - 3.27478i) q^{66} +(9.86074 + 5.69310i) q^{67} -1.09825i q^{68} +6.85951i q^{69} +(-3.72739 - 2.15201i) q^{70} +(-1.61897 + 0.934712i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-4.66802 + 2.69509i) q^{73} +(-2.42528 + 1.40024i) q^{74} -6.88681i q^{75} +(-4.26699 + 0.890378i) q^{76} +(-3.86822 + 1.47630i) q^{77} +(1.42353 - 0.821877i) q^{78} +(-5.22027 - 9.04178i) q^{79} +(1.72386 - 2.98582i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.04813 - 3.54746i) q^{82} +4.26934i q^{83} +1.24837 q^{84} +(-3.27919 - 1.89324i) q^{85} +(-1.73718 - 1.00296i) q^{86} -1.53213i q^{87} +(-1.18259 - 3.09863i) q^{88} +(-9.98398 - 5.76425i) q^{89} +(1.72386 + 2.98582i) q^{90} +(-1.77709 - 1.02600i) q^{91} +(3.42976 + 5.94051i) q^{92} +(1.31071 + 2.27022i) q^{93} +0.772098 q^{94} +(-4.69720 + 14.2754i) q^{95} +1.00000i q^{96} +(-3.47315 + 2.00523i) q^{97} +(2.72079 + 4.71255i) q^{98} +(3.27478 + 0.525163i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 20 q^{2} - 20 q^{4} - 4 q^{5} - 40 q^{8} + 20 q^{9} + 4 q^{10} - 10 q^{13} + 12 q^{14} - 12 q^{15} - 20 q^{16} - 6 q^{17} + 40 q^{18} + 10 q^{19} + 8 q^{20} - 2 q^{21} + 8 q^{23} - 8 q^{25} - 20 q^{26}+ \cdots - 30 q^{98}+O(q^{100}) $ 40 * q + 20 * q^2 - 20 * q^4 - 4 * q^5 - 40 * q^8 + 20 * q^9 + 4 * q^10 - 10 * q^13 + 12 * q^14 - 12 * q^15 - 20 * q^16 - 6 * q^17 + 40 * q^18 + 10 * q^19 + 8 * q^20 - 2 * q^21 + 8 * q^23 - 8 * q^25 - 20 * q^26 + 12 * q^28 - 4 * q^29 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 12 * q^35 + 20 * q^36 + 8 * q^38 + 4 * q^40 + 2 * q^42 - 6 * q^43 - 8 * q^45 + 16 * q^46 + 10 * q^47 - 60 * q^49 - 16 * q^50 + 4 * q^51 - 10 * q^52 + 48 * q^53 + 16 * q^55 - 14 * q^57 - 8 * q^58 + 12 * q^60 - 6 * q^61 - 12 * q^63 + 40 * q^64 + 24 * q^65 - 4 * q^66 - 60 * q^67 + 12 * q^70 - 66 * q^71 - 20 * q^72 + 48 * q^73 + 12 * q^74 - 2 * q^76 + 8 * q^77 + 48 * q^79 - 4 * q^80 - 20 * q^81 + 4 * q^84 + 24 * q^85 - 6 * q^86 - 42 * q^89 - 4 * q^90 + 8 * q^92 - 12 * q^93 + 20 * q^94 - 8 * q^95 - 30 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1254\mathbb{Z}\right)^\times$.

$n$	$343$	$419$	$1123$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.72386	+	2.98582i	0.770935	+	1.33530i	0.937051	+	0.349192i	$0.113544\pi$
$5$	1.72386	+	2.98582i	0.770935	+	1.33530i	−0.166116	+	0.986106i	$0.553123\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$			1.24837i			0.471838i	0.971773	+	0.235919i	$0.0758100\pi$
$7$			1.24837i			0.471838i	−0.971773	+	0.235919i	$0.924190\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.72386	+	2.98582i	−0.545133	+	0.944198i
$11$	1.18259	+	3.09863i	0.356563	+	0.934271i
$11$	1.18259	+	3.09863i	0.356563	+	0.934271i
$12$		−	1.00000i		−	0.288675i
$13$	−0.821877	+	1.42353i	−0.227948	+	0.394817i	−0.957200	−	0.289428i	$-0.906535\pi$
$13$	−0.821877	+	1.42353i	−0.227948	+	0.394817i	0.729252	+	0.684245i	$0.239868\pi$
$14$	−1.08112	+	0.624183i	−0.288941	+	0.166820i
$15$	−2.98582	−	1.72386i	−0.770935	−	0.445099i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.951116	+	0.549127i	−0.230679	+	0.133183i	−0.610885	−	0.791719i	$-0.709186\pi$
$17$	−0.951116	+	0.549127i	−0.230679	+	0.133183i	0.380206	+	0.924902i	$0.375853\pi$
$18$	1.00000			0.235702
$19$	2.90459	+	3.25014i	0.666358	+	0.745632i
$19$	2.90459	+	3.25014i	0.666358	+	0.745632i
$20$	−3.44773			−0.770935
$21$	−0.624183	−	1.08112i	−0.136208	−	0.235919i
$22$	−2.09220	+	2.57346i	−0.446058	+	0.548664i
$23$	3.42976	−	5.94051i	0.715154	−	1.23868i	−0.247746	−	0.968825i	$-0.579690\pi$
$23$	3.42976	−	5.94051i	0.715154	−	1.23868i	0.962900	−	0.269858i	$-0.0869767\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$	−3.44340	+	5.96415i	−0.688681	+	1.19283i
$26$	−1.64375			−0.322367
$27$			1.00000i			0.192450i
$28$	−1.08112	−	0.624183i	−0.204312	−	0.117960i
$29$	−0.766066	+	1.32687i	−0.142255	+	0.246393i	−0.928345	−	0.371719i	$-0.878769\pi$
$29$	−0.766066	+	1.32687i	−0.142255	+	0.246393i	0.786091	+	0.618111i	$0.212102\pi$
$30$		−	3.44773i		−	0.629466i
$31$		−	2.62142i		−	0.470821i	−0.971896	−	0.235411i	$-0.924357\pi$
$31$		−	2.62142i		−	0.470821i	0.971896	−	0.235411i	$-0.0756435\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−2.57346	−	2.09220i	−0.447983	−	0.364205i
$34$	−0.951116	−	0.549127i	−0.163115	−	0.0941745i
$35$	−3.72739	+	2.15201i	−0.630045	+	0.363756i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$			2.80047i			0.460395i	0.973144	+	0.230197i	$0.0739372\pi$
$37$			2.80047i			0.460395i	−0.973144	+	0.230197i	$0.926063\pi$
$38$	−1.36241	+	4.14051i	−0.221012	+	0.671680i
$39$		−	1.64375i		−	0.263211i
$40$	−1.72386	−	2.98582i	−0.272567	−	0.472099i
$41$	−2.04813	−	3.54746i	−0.319864	−	0.554020i	0.660596	−	0.750742i	$-0.270304\pi$
$41$	−2.04813	−	3.54746i	−0.319864	−	0.554020i	−0.980459	+	0.196722i	$0.936970\pi$
$42$	0.624183	−	1.08112i	0.0963135	−	0.166820i
$43$	−1.73718	+	1.00296i	−0.264917	+	0.152950i	−0.626575	−	0.779361i	$-0.715544\pi$
$43$	−1.73718	+	1.00296i	−0.264917	+	0.152950i	0.361659	+	0.932311i	$0.382211\pi$
$44$	−3.27478	−	0.525163i	−0.493692	−	0.0791713i
$45$	3.44773			0.513957
$46$	6.85951			1.01138
$47$	0.386049	−	0.668656i	0.0563110	−	0.0975335i	−0.836496	−	0.547973i	$-0.815399\pi$
$47$	0.386049	−	0.668656i	0.0563110	−	0.0975335i	0.892807	+	0.450440i	$0.148733\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	5.44158			0.777369
$50$	−6.88681			−0.973942
$51$	0.549127	−	0.951116i	0.0768932	−	0.133183i
$52$	−0.821877	−	1.42353i	−0.113974	−	0.197409i
$53$	−7.64033	−	4.41114i	−1.04948	−	0.605917i	−0.126976	−	0.991906i	$-0.540527\pi$
$53$	−7.64033	−	4.41114i	−1.04948	−	0.605917i	−0.922504	+	0.385989i	$0.873860\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−7.21332	+	8.87260i	−0.972643	+	1.19638i
$56$		−	1.24837i		−	0.166820i
$57$	−4.14051	−	1.36241i	−0.548424	−	0.180455i
$58$	−1.53213			−0.201179
$59$	7.93429	−	4.58086i	1.03296	−	0.596378i	0.115126	−	0.993351i	$-0.463273\pi$
$59$	7.93429	−	4.58086i	1.03296	−	0.596378i	0.917830	+	0.396973i	$0.129939\pi$
$60$	2.98582	−	1.72386i	0.385467	−	0.222550i
$61$	−4.04837	−	2.33733i	−0.518341	−	0.299264i	0.217915	−	0.975968i	$-0.430075\pi$
$61$	−4.04837	−	2.33733i	−0.518341	−	0.299264i	−0.736256	+	0.676704i	$0.763408\pi$
$62$	2.27022	−	1.31071i	0.288318	−	0.166460i
$63$	1.08112	+	0.624183i	0.136208	+	0.0786397i
$64$	1.00000			0.125000
$65$	−5.66721			−0.702931
$66$	0.525163	−	3.27478i	0.0646431	−	0.403098i
$67$	9.86074	+	5.69310i	1.20468	+	0.695523i	0.961592	−	0.274481i	$-0.0885061\pi$
$67$	9.86074	+	5.69310i	1.20468	+	0.695523i	0.243089	+	0.970004i	$0.421839\pi$
$68$		−	1.09825i		−	0.133183i
$69$			6.85951i			0.825788i
$70$	−3.72739	−	2.15201i	−0.445509	−	0.257215i
$71$	−1.61897	+	0.934712i	−0.192136	+	0.110930i	−0.592982	−	0.805216i	$-0.702050\pi$
$71$	−1.61897	+	0.934712i	−0.192136	+	0.110930i	0.400846	+	0.916145i	$0.368716\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−4.66802	+	2.69509i	−0.546351	+	0.315436i	−0.747649	−	0.664094i	$-0.768817\pi$
$73$	−4.66802	+	2.69509i	−0.546351	+	0.315436i	0.201298	+	0.979530i	$0.435484\pi$
$74$	−2.42528	+	1.40024i	−0.281933	+	0.162774i
$75$		−	6.88681i		−	0.795220i
$76$	−4.26699	+	0.890378i	−0.489458	+	0.102133i
$77$	−3.86822	+	1.47630i	−0.440825	+	0.168240i
$78$	1.42353	−	0.821877i	0.161183	−	0.0930593i
$79$	−5.22027	−	9.04178i	−0.587327	−	1.01728i	−0.994581	−	0.103965i	$-0.966847\pi$
$79$	−5.22027	−	9.04178i	−0.587327	−	1.01728i	0.407254	−	0.913315i	$-0.366486\pi$
$80$	1.72386	−	2.98582i	0.192734	−	0.333825i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.04813	−	3.54746i	0.226178	−	0.391751i
$83$			4.26934i			0.468621i	0.972162	+	0.234310i	$0.0752832\pi$
$83$			4.26934i			0.468621i	−0.972162	+	0.234310i	$0.924717\pi$
$84$	1.24837			0.136208
$85$	−3.27919	−	1.89324i	−0.355678	−	0.205351i
$86$	−1.73718	−	1.00296i	−0.187324	−	0.108152i
$87$		−	1.53213i		−	0.164262i
$88$	−1.18259	−	3.09863i	−0.126064	−	0.330315i
$89$	−9.98398	−	5.76425i	−1.05830	−	0.611010i	−0.133338	−	0.991071i	$-0.542570\pi$
$89$	−9.98398	−	5.76425i	−1.05830	−	0.611010i	−0.924961	+	0.380061i	$0.875903\pi$
$90$	1.72386	+	2.98582i	0.181711	+	0.314733i
$91$	−1.77709	−	1.02600i	−0.186290	−	0.107554i
$92$	3.42976	+	5.94051i	0.357577	+	0.619341i
$93$	1.31071	+	2.27022i	0.135914	+	0.235411i
$94$	0.772098			0.0796358
$95$	−4.69720	+	14.2754i	−0.481923	+	1.46462i
$96$			1.00000i			0.102062i
$97$	−3.47315	+	2.00523i	−0.352645	+	0.203600i	−0.665850	−	0.746086i	$-0.731931\pi$
$97$	−3.47315	+	2.00523i	−0.352645	+	0.203600i	0.313204	+	0.949686i	$0.398598\pi$
$98$	2.72079	+	4.71255i	0.274841	+	0.476039i
$99$	3.27478	+	0.525163i	0.329128	+	0.0527808i
$100$	−3.44340	−	5.96415i	−0.344340	−	0.596415i
$101$	1.66293	+	0.960091i	0.165467	+	0.0955327i	0.580447	−	0.814298i	$-0.302878\pi$
$101$	1.66293	+	0.960091i	0.165467	+	0.0955327i	−0.414979	+	0.909831i	$0.636211\pi$
$102$	1.09825			0.108743
$103$		−	0.580029i		−	0.0571520i	−0.999592	−	0.0285760i	$-0.990903\pi$
$103$		−	0.580029i		−	0.0571520i	0.999592	−	0.0285760i	$-0.00909726\pi$
$104$	0.821877	−	1.42353i	0.0805917	−	0.139589i
$105$	2.15201	−	3.72739i	0.210015	−	0.363756i
$106$		−	8.82229i		−	0.856896i
$107$	−1.50856			−0.145838			−0.0729189	−	0.997338i	$-0.523231\pi$
$107$	−1.50856			−0.145838			−0.0729189	+	0.997338i	$0.523231\pi$
$108$	−0.866025	−	0.500000i	−0.0833333	−	0.0481125i
$109$	−3.11316	−	5.39214i	−0.298186	−	0.516474i	0.677535	−	0.735491i	$-0.263048\pi$
$109$	−3.11316	−	5.39214i	−0.298186	−	0.516474i	−0.975721	+	0.219017i	$0.929715\pi$
$110$	−11.2906	−	1.81062i	−1.07651	−	0.172636i
$111$	−1.40024	−	2.42528i	−0.132904	−	0.230197i
$112$	1.08112	−	0.624183i	0.102156	−	0.0589798i
$113$		−	7.42260i		−	0.698260i	−0.937074	−	0.349130i	$-0.886477\pi$
$113$		−	7.42260i		−	0.698260i	0.937074	−	0.349130i	$-0.113523\pi$
$114$	−0.890378	−	4.26699i	−0.0833915	−	0.399640i
$115$	23.6497			2.20535
$116$	−0.766066	−	1.32687i	−0.0711275	−	0.123196i
$117$	0.821877	+	1.42353i	0.0759826	+	0.131606i
$118$	7.93429	+	4.58086i	0.730411	+	0.421703i
$119$	−0.685511	−	1.18734i	−0.0628407	−	0.108843i
$120$	2.98582	+	1.72386i	0.272567	+	0.157366i
$121$	−8.20297	+	7.32879i	−0.745725	+	0.666254i
$122$		−	4.67466i		−	0.423224i
$123$	3.54746	+	2.04813i	0.319864	+	0.184673i
$124$	2.27022	+	1.31071i	0.203872	+	0.117705i
$125$	−6.50520			−0.581843
$126$			1.24837i			0.111213i
$127$	5.76857	−	9.99146i	0.511878	−	0.886599i	−0.488027	−	0.872829i	$-0.662283\pi$
$127$	5.76857	−	9.99146i	0.511878	−	0.886599i	0.999905	−	0.0137705i	$-0.00438342\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	1.00296	−	1.73718i	0.0883056	−	0.152950i
$130$	−2.83361	−	4.90795i	−0.248524	−	0.430456i
$131$	−6.23545	+	3.60004i	−0.544794	+	0.314537i	−0.747020	−	0.664802i	$-0.768516\pi$
$131$	−6.23545	+	3.60004i	−0.544794	+	0.314537i	0.202226	+	0.979339i	$0.435183\pi$
$132$	3.09863	−	1.18259i	0.269701	−	0.102931i
$133$	−4.05736	+	3.62599i	−0.351818	+	0.314413i
$134$			11.3862i			0.983618i
$135$	−2.98582	+	1.72386i	−0.256978	+	0.148366i
$136$	0.951116	−	0.549127i	0.0815575	−	0.0470872i
$137$	−1.01202	+	1.75287i	−0.0864627	+	0.149758i	−0.906014	−	0.423249i	$-0.860890\pi$
$137$	−1.01202	+	1.75287i	−0.0864627	+	0.149758i	0.819551	+	0.573006i	$0.194223\pi$
$138$	−5.94051	+	3.42976i	−0.505690	+	0.291960i
$139$	19.1914	+	11.0802i	1.62779	+	0.939806i	0.984750	+	0.173975i	$0.0556613\pi$
$139$	19.1914	+	11.0802i	1.62779	+	0.939806i	0.643042	+	0.765831i	$0.277672\pi$
$140$		−	4.30402i		−	0.363756i
$141$			0.772098i			0.0650224i
$142$	−1.61897	−	0.934712i	−0.135861	−	0.0784393i
$143$	−5.38294	−	0.863238i	−0.450144	−	0.0721876i
$144$	−1.00000			−0.0833333
$145$	−5.28237			−0.438677
$146$	−4.66802	−	2.69509i	−0.386328	−	0.223047i
$147$	−4.71255	+	2.72079i	−0.388684	+	0.224407i
$148$	−2.42528	−	1.40024i	−0.199357	−	0.115099i
$149$	−16.8557	+	9.73163i	−1.38087	+	0.797246i	−0.992263	−	0.124157i	$-0.960377\pi$
$149$	−16.8557	+	9.73163i	−1.38087	+	0.797246i	−0.388608	+	0.921403i	$0.627044\pi$
$150$	5.96415	−	3.44340i	0.486971	−	0.281153i
$151$	13.2156			1.07547			0.537733	−	0.843115i	$-0.319281\pi$
$151$	13.2156			1.07547			0.537733	+	0.843115i	$0.319281\pi$
$152$	−2.90459	−	3.25014i	−0.235593	−	0.263621i
$153$			1.09825i			0.0887886i
$154$	−3.21263	−	2.61183i	−0.258881	−	0.210467i
$155$	7.82709	−	4.51897i	0.628687	−	0.362972i
$156$	1.42353	+	0.821877i	0.113974	+	0.0658028i
$157$	5.27038	+	9.12857i	0.420622	+	0.728539i	0.996000	−	0.0893485i	$-0.0284785\pi$
$157$	5.27038	+	9.12857i	0.420622	+	0.728539i	−0.575378	+	0.817887i	$0.695145\pi$
$158$	5.22027	−	9.04178i	0.415303	−	0.719325i
$159$	8.82229			0.699653
$160$	3.44773			0.272567
$161$	7.41594	+	4.28159i	0.584458	+	0.337437i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	1.16899			0.0915625			0.0457812	−	0.998951i	$-0.485422\pi$
$163$	1.16899			0.0915625			0.0457812	+	0.998951i	$0.485422\pi$
$164$	4.09625			0.319864
$165$	1.81062	−	11.2906i	0.140956	−	0.878968i
$166$	−3.69736	+	2.13467i	−0.286971	+	0.165683i
$167$	−3.26312	+	5.65190i	−0.252508	+	0.437357i	−0.964216	−	0.265119i	$-0.914589\pi$
$167$	−3.26312	+	5.65190i	−0.252508	+	0.437357i	0.711708	+	0.702476i	$0.247922\pi$
$168$	0.624183	+	1.08112i	0.0481568	+	0.0834100i
$169$	5.14904	+	8.91839i	0.396080	+	0.686030i
$170$		−	3.78648i		−	0.290410i
$171$	4.26699	−	0.890378i	0.326305	−	0.0680889i
$172$		−	2.00592i		−	0.152950i
$173$	7.99835	+	13.8536i	0.608104	+	1.05327i	0.991553	+	0.129704i	$0.0414028\pi$
$173$	7.99835	+	13.8536i	0.608104	+	1.05327i	−0.383449	+	0.923562i	$0.625264\pi$
$174$	1.32687	−	0.766066i	0.100589	−	0.0580753i
$175$	−7.44545	−	4.29863i	−0.562823	−	0.324946i
$176$	2.09220	−	2.57346i	0.157705	−	0.193982i
$177$	−4.58086	+	7.93429i	−0.344319	+	0.596378i
$178$		−	11.5285i		−	0.864098i
$179$			10.4097i			0.778060i	0.921225	+	0.389030i	$0.127190\pi$
$179$			10.4097i			0.778060i	−0.921225	+	0.389030i	$0.872810\pi$
$180$	−1.72386	+	2.98582i	−0.128489	+	0.222550i
$181$	22.7100	+	13.1116i	1.68802	+	0.974579i	0.956032	+	0.293262i	$0.0947409\pi$
$181$	22.7100	+	13.1116i	1.68802	+	0.974579i	0.731989	+	0.681317i	$0.238592\pi$
$182$		−	2.05201i		−	0.152105i
$183$	4.67466			0.345561
$184$	−3.42976	+	5.94051i	−0.252845	+	0.437940i
$185$	−8.36170	+	4.82763i	−0.614764	+	0.354934i
$186$	−1.31071	+	2.27022i	−0.0961060	+	0.166460i
$187$	−2.82632	−	2.29776i	−0.206681	−	0.168029i
$188$	0.386049	+	0.668656i	0.0281555	+	0.0487668i
$189$	−1.24837			−0.0908053
$190$	−14.7114	+	3.06978i	−1.06728	+	0.222705i
$191$	20.3253			1.47069			0.735344	−	0.677694i	$-0.237020\pi$
$191$	20.3253			1.47069			0.735344	+	0.677694i	$0.237020\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	1.39463	+	2.41558i	0.100388	+	0.173877i	0.911845	−	0.410536i	$-0.134658\pi$
$193$	1.39463	+	2.41558i	0.100388	+	0.173877i	−0.811457	+	0.584413i	$0.801325\pi$
$194$	−3.47315	−	2.00523i	−0.249358	−	0.143967i
$195$	4.90795	−	2.83361i	0.351466	−	0.202919i
$196$	−2.72079	+	4.71255i	−0.194342	+	0.336611i
$197$		−	8.06663i		−	0.574724i	−0.957822	−	0.287362i	$-0.907222\pi$
$197$		−	8.06663i		−	0.574724i	0.957822	−	0.287362i	$-0.0927782\pi$
$198$	1.18259	+	3.09863i	0.0840428	+	0.220210i
$199$	6.83492	−	11.8384i	0.484514	−	0.839204i	−0.515327	−	0.856993i	$-0.672330\pi$
$199$	6.83492	−	11.8384i	0.484514	−	0.839204i	0.999842	+	0.0177898i	$0.00566297\pi$
$200$	3.44340	−	5.96415i	0.243485	−	0.421729i
$201$	−11.3862			−0.803121
$202$			1.92018i			0.135104i
$203$	−1.65641	−	0.956331i	−0.116257	−	0.0671213i
$204$	0.549127	+	0.951116i	0.0384466	+	0.0665914i
$205$	7.06138	−	12.2307i	0.493188	−	0.854227i
$206$	0.502320	−	0.290015i	0.0349983	−	0.0202063i
$207$	−3.42976	−	5.94051i	−0.238385	−	0.412894i
$208$	1.64375			0.113974
$209$	−6.63603	+	12.8438i	−0.459024	+	0.888424i
$210$	4.30402			0.297006
$211$	−9.65373	−	16.7208i	−0.664590	−	1.15110i	−0.979396	−	0.201948i	$-0.935273\pi$
$211$	−9.65373	−	16.7208i	−0.664590	−	1.15110i	0.314806	−	0.949156i	$-0.398061\pi$
$212$	7.64033	−	4.41114i	0.524740	−	0.302959i
$213$	0.934712	−	1.61897i	0.0640454	−	0.110930i
$214$	−0.754278	−	1.30645i	−0.0515614	−	0.0893070i
$215$	−5.98930	−	3.45793i	−0.408467	−	0.235829i
$216$		−	1.00000i		−	0.0680414i
$217$	3.27249			0.222151
$218$	3.11316	−	5.39214i	0.210849	−	0.365202i
$219$	2.69509	−	4.66802i	0.182117	−	0.315436i
$220$	−4.07724	−	10.6832i	−0.274887	−	0.720262i
$221$		−	1.80526i		−	0.121435i
$222$	1.40024	−	2.42528i	0.0939777	−	0.162774i
$223$	−5.48809	+	3.16855i	−0.367510	+	0.212182i	−0.672370	−	0.740215i	$-0.734724\pi$
$223$	−5.48809	+	3.16855i	−0.367510	+	0.212182i	0.304860	+	0.952397i	$0.401390\pi$
$224$	1.08112	+	0.624183i	0.0722352	+	0.0417050i
$225$	3.44340	+	5.96415i	0.229560	+	0.397610i
$226$	6.42816	−	3.71130i	0.427595	−	0.246872i
$227$	17.4617			1.15897			0.579486	−	0.814982i	$-0.303253\pi$
$227$	17.4617			1.15897			0.579486	+	0.814982i	$0.303253\pi$
$228$	3.25014	−	2.90459i	0.215245	−	0.192361i
$229$	26.2752			1.73632			0.868158	−	0.496287i	$-0.165304\pi$
$229$	26.2752			1.73632			0.868158	+	0.496287i	$0.165304\pi$
$230$	11.8249	+	20.4813i	0.779708	+	1.35049i
$231$	2.61183	−	3.21263i	0.171846	−	0.211375i
$232$	0.766066	−	1.32687i	0.0502947	−	0.0871130i
$233$	6.90824	−	3.98847i	0.452574	−	0.261294i	−0.256343	−	0.966586i	$-0.582518\pi$
$233$	6.90824	−	3.98847i	0.452574	−	0.261294i	0.708917	+	0.705292i	$0.249184\pi$
$234$	−0.821877	+	1.42353i	−0.0537278	+	0.0930593i
$235$	2.66198			0.173648
$236$			9.16173i			0.596378i
$237$	9.04178	+	5.22027i	0.587327	+	0.339093i
$238$	0.685511	−	1.18734i	0.0444351	−	0.0769639i
$239$			4.21658i			0.272748i	0.990657	+	0.136374i	$0.0435449\pi$
$239$			4.21658i			0.272748i	−0.990657	+	0.136374i	$0.956455\pi$
$240$			3.44773i			0.222550i
$241$	13.7940	−	23.8920i	0.888552	−	1.53902i	0.0469650	−	0.998897i	$-0.485045\pi$
$241$	13.7940	−	23.8920i	0.888552	−	1.53902i	0.841587	−	0.540121i	$-0.181622\pi$
$242$	−10.4484	−	3.43959i	−0.671649	−	0.221105i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	4.04837	−	2.33733i	0.259170	−	0.149632i
$245$	9.38054	+	16.2476i	0.599301	+	1.03802i
$246$			4.09625i			0.261168i
$247$	−7.01389	+	1.46356i	−0.446283	+	0.0931243i
$248$			2.62142i			0.166460i
$249$	−2.13467	−	3.69736i	−0.135279	−	0.234310i
$250$	−3.25260	−	5.63367i	−0.205713	−	0.356305i
$251$	−1.41158	+	2.44494i	−0.0890984	+	0.154323i	−0.907130	−	0.420850i	$-0.861732\pi$
$251$	−1.41158	+	2.44494i	−0.0890984	+	0.154323i	0.818032	+	0.575173i	$0.195065\pi$
$252$	−1.08112	+	0.624183i	−0.0681040	+	0.0393198i
$253$	22.4634	+	3.60236i	1.41226	+	0.226478i
$254$	11.5371			0.723905
$255$	3.78648			0.237118
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.17573	−	4.14291i	−0.447610	−	0.258428i	0.259210	−	0.965821i	$-0.416538\pi$
$257$	−7.17573	−	4.14291i	−0.447610	−	0.258428i	−0.706820	+	0.707393i	$0.749871\pi$
$258$	2.00592			0.124883
$259$	−3.49601			−0.217232
$260$	2.83361	−	4.90795i	0.175733	−	0.304378i
$261$	0.766066	+	1.32687i	0.0474183	+	0.0821309i
$262$	−6.23545	−	3.60004i	−0.385228	−	0.222411i
$263$	12.1077	−	6.99036i	0.746590	−	0.431044i	−0.0778702	−	0.996964i	$-0.524812\pi$
$263$	12.1077	−	6.99036i	0.746590	−	0.431044i	0.824461	+	0.565919i	$0.191479\pi$
$264$	2.57346	+	2.09220i	0.158386	+	0.128766i
$265$		−	30.4168i		−	1.86849i
$266$	−5.16888	−	1.70078i	−0.316924	−	0.104282i
$267$	11.5285			0.705533
$268$	−9.86074	+	5.69310i	−0.602341	+	0.347761i
$269$	−7.21175	+	4.16371i	−0.439708	+	0.253866i	−0.703474	−	0.710721i	$-0.748369\pi$
$269$	−7.21175	+	4.16371i	−0.439708	+	0.253866i	0.263766	+	0.964587i	$0.415035\pi$
$270$	−2.98582	−	1.72386i	−0.181711	−	0.104911i
$271$	25.3510	−	14.6364i	1.53996	−	0.889097i	0.541122	−	0.840944i	$-0.318000\pi$
$271$	25.3510	−	14.6364i	1.53996	−	0.889097i	0.998840	−	0.0481531i	$-0.0153336\pi$
$272$	0.951116	+	0.549127i	0.0576699	+	0.0332957i
$273$	2.05201			0.124193
$274$	−2.02404			−0.122277
$275$	−22.5528	−	3.61670i	−1.35999	−	0.218095i
$276$	−5.94051	−	3.42976i	−0.357577	−	0.206447i
$277$			11.2396i			0.675324i	0.941267	+	0.337662i	$0.109636\pi$
$277$			11.2396i			0.675324i	−0.941267	+	0.337662i	$0.890364\pi$
$278$			22.1603i			1.32909i
$279$	−2.27022	−	1.31071i	−0.135914	−	0.0784702i
$280$	3.72739	−	2.15201i	0.222754	−	0.128607i
$281$	6.56974	−	11.3791i	0.391918	−	0.678821i	−0.600785	−	0.799411i	$-0.705145\pi$
$281$	6.56974	−	11.3791i	0.391918	−	0.678821i	0.992702	+	0.120589i	$0.0384785\pi$
$282$	−0.668656	+	0.386049i	−0.0398179	+	0.0229889i
$283$	−12.2273	+	7.05943i	−0.726837	+	0.419640i	−0.817264	−	0.576263i	$-0.804510\pi$
$283$	−12.2273	+	7.05943i	−0.726837	+	0.419640i	0.0904266	+	0.995903i	$0.471177\pi$
$284$		−	1.86942i		−	0.110930i
$285$	−3.06978	−	14.7114i	−0.181838	−	0.871429i
$286$	−1.94388	−	5.09338i	−0.114944	−	0.301178i
$287$	4.42853	−	2.55681i	0.261408	−	0.150924i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−7.89692	+	13.6779i	−0.464525	+	0.804580i
$290$	−2.64119	−	4.57467i	−0.155096	−	0.268634i
$291$	2.00523	−	3.47315i	0.117548	−	0.203600i
$292$		−	5.39017i		−	0.315436i
$293$	−24.5703			−1.43541			−0.717705	−	0.696347i	$-0.754807\pi$
$293$	−24.5703			−1.43541			−0.717705	+	0.696347i	$0.754807\pi$
$294$	−4.71255	−	2.72079i	−0.274841	−	0.158680i
$295$	27.3553	+	15.7936i	1.59268	+	0.919537i
$296$		−	2.80047i		−	0.162774i
$297$	−3.09863	+	1.18259i	−0.179801	+	0.0686207i
$298$	−16.8557	−	9.73163i	−0.976423	−	0.563738i
$299$	5.63768	+	9.76474i	0.326035	+	0.564710i
$300$	5.96415	+	3.44340i	0.344340	+	0.198805i
$301$	−1.25206	−	2.16863i	−0.0721675	−	0.124998i
$302$	6.60778	+	11.4450i	0.380235	+	0.658586i
$303$	−1.92018			−0.110312
$304$	1.36241	−	4.14051i	0.0781394	−	0.237475i
$305$		−	16.1169i		−	0.922853i
$306$	−0.951116	+	0.549127i	−0.0543717	+	0.0313915i
$307$	8.36440	+	14.4876i	0.477381	+	0.826849i	0.999664	−	0.0259236i	$-0.00825265\pi$
$307$	8.36440	+	14.4876i	0.477381	+	0.826849i	−0.522282	+	0.852773i	$0.674919\pi$
$308$	0.655595	−	4.08813i	0.0373560	−	0.232943i
$309$	0.290015	+	0.502320i	0.0164984	+	0.0285760i
$310$	7.82709	+	4.51897i	0.444549	+	0.256660i
$311$	27.5985			1.56497			0.782484	−	0.622671i	$-0.213953\pi$
$311$	27.5985			1.56497			0.782484	+	0.622671i	$0.213953\pi$
$312$			1.64375i			0.0930593i
$313$	−6.53619	+	11.3210i	−0.369447	+	0.639901i	−0.989479	−	0.144675i	$-0.953786\pi$
$313$	−6.53619	+	11.3210i	−0.369447	+	0.639901i	0.620032	+	0.784577i	$0.287120\pi$
$314$	−5.27038	+	9.12857i	−0.297425	+	0.515155i
$315$			4.30402i			0.242504i
$316$	10.4405			0.587327
$317$	−25.2620	−	14.5850i	−1.41885	−	0.819176i	−0.422656	−	0.906290i	$-0.638902\pi$
$317$	−25.2620	−	14.5850i	−1.41885	−	0.819176i	−0.996198	+	0.0871138i	$0.972236\pi$
$318$	4.41114	+	7.64033i	0.247365	+	0.428448i
$319$	−5.01740	−	0.804619i	−0.280921	−	0.0450500i
$320$	1.72386	+	2.98582i	0.0963669	+	0.166912i
$321$	1.30645	−	0.754278i	0.0729189	−	0.0420997i
$322$			8.56319i			0.477208i
$323$	−4.54733	−	1.49627i	−0.253020	−	0.0832546i
$324$	1.00000			0.0555556
$325$	−5.66011	−	9.80360i	−0.313966	−	0.543806i
$326$	0.584496	+	1.01238i	0.0323722	+	0.0560703i
$327$	5.39214	+	3.11316i	0.298186	+	0.172158i
$328$	2.04813	+	3.54746i	0.113089	+	0.195876i
$329$	0.834728	+	0.481930i	0.0460200	+	0.0265697i
$330$	10.6832	−	4.07724i	0.588092	−	0.224444i
$331$		−	24.6409i		−	1.35438i	−0.735806	−	0.677192i	$-0.763197\pi$
$331$		−	24.6409i		−	1.35438i	0.735806	−	0.677192i	$-0.236803\pi$
$332$	−3.69736	−	2.13467i	−0.202919	−	0.117155i
$333$	2.42528	+	1.40024i	0.132904	+	0.0767324i
$334$	−6.52625			−0.357100
$335$			39.2565i			2.14481i
$336$	−0.624183	+	1.08112i	−0.0340520	+	0.0589798i
$337$	6.43400	+	11.1440i	0.350482	+	0.607053i	0.986334	−	0.164758i	$-0.0526843\pi$
$337$	6.43400	+	11.1440i	0.350482	+	0.607053i	−0.635852	+	0.771811i	$0.719351\pi$
$338$	−5.14904	+	8.91839i	−0.280071	+	0.485097i
$339$	3.71130	+	6.42816i	0.201570	+	0.349130i
$340$	3.27919	−	1.89324i	0.177839	−	0.102675i
$341$	8.12281	−	3.10006i	0.439875	−	0.167878i
$342$	2.90459	+	3.25014i	0.157062	+	0.175747i
$343$			15.5316i			0.838630i
$344$	1.73718	−	1.00296i	0.0936622	−	0.0540759i
$345$	−20.4813	+	11.8249i	−1.10267	+	0.636629i
$346$	−7.99835	+	13.8536i	−0.429994	+	0.744772i
$347$	−24.8878	+	14.3690i	−1.33605	+	0.771368i	−0.986219	−	0.165445i	$-0.947094\pi$
$347$	−24.8878	+	14.3690i	−1.33605	+	0.771368i	−0.349830	+	0.936813i	$0.613761\pi$
$348$	1.32687	+	0.766066i	0.0711275	+	0.0410655i
$349$			13.6949i			0.733070i	0.930404	+	0.366535i	$0.119456\pi$
$349$			13.6949i			0.733070i	−0.930404	+	0.366535i	$0.880544\pi$
$350$		−	8.59726i		−	0.459543i
$351$	−1.42353	−	0.821877i	−0.0759826	−	0.0438686i
$352$	3.27478	+	0.525163i	0.174547	+	0.0279913i
$353$	−14.2208			−0.756895			−0.378448	−	0.925623i	$-0.623542\pi$
$353$	−14.2208			−0.756895			−0.378448	+	0.925623i	$0.623542\pi$
$354$	−9.16173			−0.486940
$355$	−5.58176	−	3.22263i	−0.296249	−	0.171039i
$356$	9.98398	−	5.76425i	0.529150	−	0.305505i
$357$	1.18734	+	0.685511i	0.0628407	+	0.0362811i
$358$	−9.01509	+	5.20486i	−0.476462	+	0.275086i
$359$	−15.7117	+	9.07113i	−0.829230	+	0.478756i	−0.853589	−	0.520947i	$-0.825579\pi$
$359$	−15.7117	+	9.07113i	−0.829230	+	0.478756i	0.0243591	+	0.999703i	$0.492245\pi$
$360$	−3.44773			−0.181711
$361$	−2.12676	+	18.8806i	−0.111935	+	0.993716i
$362$			26.2232i			1.37826i
$363$	3.43959	−	10.4484i	0.180532	−	0.548399i
$364$	1.77709	−	1.02600i	0.0931448	−	0.0537772i
$365$	−16.0941	−	9.29191i	−0.842402	−	0.486361i
$366$	2.33733	+	4.04837i	0.122174	+	0.211612i
$367$	2.48444	−	4.30317i	0.129687	−	0.224624i	−0.793869	−	0.608089i	$-0.791936\pi$
$367$	2.48444	−	4.30317i	0.129687	−	0.224624i	0.923555	+	0.383466i	$0.125270\pi$
$368$	−6.85951			−0.357577
$369$	−4.09625			−0.213242
$370$	−8.36170	−	4.82763i	−0.434704	−	0.250976i
$371$	5.50672	−	9.53792i	0.285895	−	0.495184i
$372$	−2.62142			−0.135914
$373$	30.2547			1.56653			0.783264	−	0.621689i	$-0.213553\pi$
$373$	30.2547			1.56653			0.783264	+	0.621689i	$0.213553\pi$
$374$	0.576762	−	3.59654i	0.0298237	−	0.185973i
$375$	5.63367	−	3.25260i	0.290921	−	0.167964i
$376$	−0.386049	+	0.668656i	−0.0199090	+	0.0344833i
$377$	−1.25922	−	2.18104i	−0.0648534	−	0.112329i
$378$	−0.624183	−	1.08112i	−0.0321045	−	0.0556066i
$379$			23.0880i			1.18595i	0.805221	+	0.592975i	$0.202047\pi$
$379$			23.0880i			1.18595i	−0.805221	+	0.592975i	$0.797953\pi$
$380$	−10.0142	−	11.2056i	−0.513718	−	0.574834i
$381$			11.5371i			0.591066i
$382$	10.1627	+	17.6022i	0.519967	+	0.900609i
$383$	4.34845	−	2.51058i	0.222196	−	0.128285i	−0.384771	−	0.923012i	$-0.625720\pi$
$383$	4.34845	−	2.51058i	0.222196	−	0.128285i	0.606967	+	0.794727i	$0.292386\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$	−11.0762	−	9.00486i	−0.564498	−	0.458930i
$386$	−1.39463	+	2.41558i	−0.0709850	+	0.122950i
$387$			2.00592i			0.101967i
$388$		−	4.01045i		−	0.203600i
$389$	6.18511	−	10.7129i	0.313597	−	0.543167i	−0.665541	−	0.746361i	$-0.731799\pi$
$389$	6.18511	−	10.7129i	0.313597	−	0.543167i	0.979138	+	0.203195i	$0.0651324\pi$
$390$	4.90795	+	2.83361i	0.248524	+	0.143485i
$391$			7.53349i			0.380985i
$392$	−5.44158			−0.274841
$393$	3.60004	−	6.23545i	0.181598	−	0.314537i
$394$	6.98591	−	4.03331i	0.351945	−	0.203195i
$395$	17.9981	−	31.1736i	0.905581	−	1.56851i
$396$	−2.09220	+	2.57346i	−0.105137	+	0.129321i
$397$	−8.99311	−	15.5765i	−0.451351	−	0.781763i	0.547119	−	0.837055i	$-0.315724\pi$
$397$	−8.99311	−	15.5765i	−0.451351	−	0.781763i	−0.998470	+	0.0552916i	$0.982391\pi$
$398$	13.6698			0.685207
$399$	1.70078	−	5.16888i	0.0851456	−	0.258767i
$400$	6.88681			0.344340
$401$	−22.0003	+	12.7019i	−1.09864	+	0.634303i	−0.935865	−	0.352360i	$-0.885379\pi$
$401$	−22.0003	+	12.7019i	−1.09864	+	0.634303i	−0.162780	+	0.986662i	$0.552046\pi$
$402$	−5.69310	−	9.86074i	−0.283946	−	0.491809i
$403$	3.73168	+	2.15449i	0.185888	+	0.107323i
$404$	−1.66293	+	0.960091i	−0.0827337	+	0.0477663i
$405$	1.72386	−	2.98582i	0.0856594	−	0.148366i
$406$		−	1.91266i		−	0.0949238i
$407$	−8.67761	+	3.31180i	−0.430133	+	0.164160i
$408$	−0.549127	+	0.951116i	−0.0271858	+	0.0470872i
$409$	−6.03359	+	10.4505i	−0.298342	+	0.516744i	−0.975757	−	0.218858i	$-0.929767\pi$
$409$	−6.03359	+	10.4505i	−0.298342	+	0.516744i	0.677415	+	0.735601i	$0.263100\pi$
$410$	14.1228			0.697473
$411$		−	2.02404i		−	0.0998385i
$412$	0.502320	+	0.290015i	0.0247475	+	0.0142880i
$413$	5.71860	+	9.90490i	0.281394	+	0.487388i
$414$	3.42976	−	5.94051i	0.168563	−	0.291960i
$415$	−12.7475	+	7.35976i	−0.625749	+	0.361276i
$416$	0.821877	+	1.42353i	0.0402958	+	0.0697944i
$417$	−22.1603			−1.08519
$418$	−14.4411	+	0.674929i	−0.706336	+	0.0330119i
$419$	−13.1385			−0.641859			−0.320930	−	0.947103i	$-0.603995\pi$
$419$	−13.1385			−0.641859			−0.320930	+	0.947103i	$0.603995\pi$
$420$	2.15201	+	3.72739i	0.105007	+	0.181878i
$421$	−2.50186	+	1.44445i	−0.121933	+	0.0703982i	−0.559726	−	0.828678i	$-0.689094\pi$
$421$	−2.50186	+	1.44445i	−0.121933	+	0.0703982i	0.437793	+	0.899076i	$0.355760\pi$
$422$	9.65373	−	16.7208i	0.469936	−	0.813954i
$423$	−0.386049	−	0.668656i	−0.0187703	−	0.0325112i
$424$	7.64033	+	4.41114i	0.371047	+	0.214224i
$425$		−	7.56347i		−	0.366882i
$426$	1.86942			0.0905739
$427$	2.91784	−	5.05385i	0.141204	−	0.244573i
$428$	0.754278	−	1.30645i	0.0364594	−	0.0631496i
$429$	5.09338	−	1.94388i	0.245911	−	0.0938516i
$430$		−	6.91585i		−	0.333512i
$431$	1.21886	−	2.11112i	0.0587103	−	0.101689i	−0.835176	−	0.549982i	$-0.814635\pi$
$431$	1.21886	−	2.11112i	0.0587103	−	0.101689i	0.893887	+	0.448293i	$0.147968\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	−28.9405	−	16.7088i	−1.39079	−	0.802973i	−0.397387	−	0.917651i	$-0.630083\pi$
$433$	−28.9405	−	16.7088i	−1.39079	−	0.802973i	−0.993403	+	0.114678i	$0.963416\pi$
$434$	1.63625	+	2.83406i	0.0785424	+	0.136039i
$435$	4.57467	−	2.64119i	0.219339	−	0.126635i
$436$	6.22631			0.298186
$437$	29.2695	−	6.10756i	1.40015	−	0.292164i
$438$	5.39017			0.257552
$439$	7.04233	+	12.1977i	0.336112	+	0.582163i	0.983698	−	0.179829i	$-0.0575545\pi$
$439$	7.04233	+	12.1977i	0.336112	+	0.582163i	−0.647586	+	0.761993i	$0.724221\pi$
$440$	7.21332	−	8.87260i	0.343881	−	0.422984i
$441$	2.72079	−	4.71255i	0.129561	−	0.224407i
$442$	1.56340	−	0.902630i	0.0743634	−	0.0429337i
$443$	1.80191	−	3.12101i	0.0856115	−	0.148283i	−0.820040	−	0.572306i	$-0.806049\pi$
$443$	1.80191	−	3.12101i	0.0856115	−	0.148283i	0.905652	+	0.424023i	$0.139382\pi$
$444$	2.80047			0.132904
$445$		−	39.7471i		−	1.88419i
$446$	−5.48809	−	3.16855i	−0.259869	−	0.150035i
$447$	9.73163	−	16.8557i	0.460290	−	0.797246i
$448$			1.24837i			0.0589798i
$449$			9.81169i			0.463042i	0.972830	+	0.231521i	$0.0743702\pi$
$449$			9.81169i			0.463042i	−0.972830	+	0.231521i	$0.925630\pi$
$450$	−3.44340	+	5.96415i	−0.162324	+	0.281153i
$451$	8.57016	−	10.5416i	0.403553	−	0.496383i
$452$	6.42816	+	3.71130i	0.302355	+	0.174565i
$453$	−11.4450	+	6.60778i	−0.537733	+	0.310460i
$454$	8.73084	+	15.1223i	0.409758	+	0.709722i
$455$		−	7.07476i		−	0.331670i
$456$	4.14051	+	1.36241i	0.193897	+	0.0638005i
$457$		−	32.2772i		−	1.50986i	−0.655803	−	0.754932i	$-0.727670\pi$
$457$		−	32.2772i		−	1.50986i	0.655803	−	0.754932i	$-0.272330\pi$
$458$	13.1376	+	22.7550i	0.613881	+	1.06327i
$459$	−0.549127	−	0.951116i	−0.0256311	−	0.0443943i
$460$	−11.8249	+	20.4813i	−0.551337	+	0.954944i
$461$	15.8758	−	9.16591i	0.739411	−	0.426899i	−0.0824442	−	0.996596i	$-0.526273\pi$
$461$	15.8758	−	9.16591i	0.739411	−	0.426899i	0.821855	+	0.569697i	$0.192939\pi$
$462$	4.08813	+	0.655595i	0.190197	+	0.0305011i
$463$	−35.9196			−1.66933			−0.834663	−	0.550761i	$-0.814338\pi$
$463$	−35.9196			−1.66933			−0.834663	+	0.550761i	$0.814338\pi$
$464$	1.53213			0.0711275
$465$	−4.51897	+	7.82709i	−0.209562	+	0.362972i
$466$	6.90824	+	3.98847i	0.320018	+	0.184762i
$467$	−31.2514			−1.44614			−0.723071	−	0.690774i	$-0.757270\pi$
$467$	−31.2514			−1.44614			−0.723071	+	0.690774i	$0.757270\pi$
$468$	−1.64375			−0.0759826
$469$	−7.10707	+	12.3098i	−0.328174	+	0.568414i
$470$	1.33099	+	2.30534i	0.0613940	+	0.106338i
$471$	−9.12857	−	5.27038i	−0.420622	−	0.242846i
$472$	−7.93429	+	4.58086i	−0.365205	+	0.210851i
$473$	−5.16216	−	4.19677i	−0.237356	−	0.192968i
$474$			10.4405i			0.479550i
$475$	−29.3860	+	6.13186i	−1.34832	+	0.281349i
$476$	1.37102			0.0628407
$477$	−7.64033	+	4.41114i	−0.349826	+	0.201972i
$478$	−3.65166	+	2.10829i	−0.167023	+	0.0964309i
$479$	22.0278	+	12.7177i	1.00648	+	0.581089i	0.910158	−	0.414262i	$-0.135960\pi$
$479$	22.0278	+	12.7177i	1.00648	+	0.581089i	0.0963174	+	0.995351i	$0.469294\pi$
$480$	−2.98582	+	1.72386i	−0.136283	+	0.0786832i
$481$	−3.98656	−	2.30164i	−0.181772	−	0.104946i
$482$	27.5881			1.25660
$483$	−8.56319			−0.389638
$484$	−2.24543	−	10.7684i	−0.102065	−	0.489472i
$485$	−11.9745	−	6.91347i	−0.543733	−	0.313924i
$486$			1.00000i			0.0453609i
$487$			21.5332i			0.975764i	0.872909	+	0.487882i	$0.162230\pi$
$487$			21.5332i			0.975764i	−0.872909	+	0.487882i	$0.837770\pi$
$488$	4.04837	+	2.33733i	0.183261	+	0.105806i
$489$	−1.01238	+	0.584496i	−0.0457812	+	0.0264318i
$490$	−9.38054	+	16.2476i	−0.423770	+	0.733990i
$491$	18.0097	−	10.3979i	0.812769	−	0.469252i	−0.0351478	−	0.999382i	$-0.511190\pi$
$491$	18.0097	−	10.3979i	0.812769	−	0.469252i	0.847916	+	0.530130i	$0.177857\pi$
$492$	−3.54746	+	2.04813i	−0.159932	+	0.0923367i
$493$		−	1.68267i		−	0.0757837i
$494$	−4.77443	−	5.34242i	−0.214812	−	0.240367i
$495$	4.07724	+	10.6832i	0.183258	+	0.480175i
$496$	−2.27022	+	1.31071i	−0.101936	+	0.0588526i
$497$	−1.16686	−	2.02107i	−0.0523410	−	0.0906572i
$498$	2.13467	−	3.69736i	0.0956568	−	0.165683i
$499$	6.60058	+	11.4325i	0.295483	+	0.511791i	0.975097	−	0.221779i	$-0.0711862\pi$
$499$	6.60058	+	11.4325i	0.295483	+	0.511791i	−0.679614	+	0.733570i	$0.737853\pi$
$500$	3.25260	−	5.63367i	0.145461	−	0.251945i
$501$		−	6.52625i		−	0.291571i
$502$	−2.82317			−0.126004
$503$	−0.888084	−	0.512736i	−0.0395977	−	0.0228618i	0.480070	−	0.877230i	$-0.340611\pi$
$503$	−0.888084	−	0.512736i	−0.0395977	−	0.0228618i	−0.519668	+	0.854368i	$0.673944\pi$
$504$	−1.08112	−	0.624183i	−0.0481568	−	0.0278033i
$505$			6.62026i			0.294598i
$506$	8.11197	+	21.2551i	0.360621	+	0.944903i
$507$	−8.91839	−	5.14904i	−0.396080	−	0.228677i
$508$	5.76857	+	9.99146i	0.255939	+	0.443299i
$509$	15.3833	+	8.88155i	0.681853	+	0.393668i	0.800553	−	0.599262i	$-0.204539\pi$
$509$	15.3833	+	8.88155i	0.681853	+	0.393668i	−0.118700	+	0.992930i	$0.537873\pi$
$510$	1.89324	+	3.27919i	0.0838340	+	0.145205i
$511$	−3.36445	−	5.82740i	−0.148835	−	0.257789i
$512$	−1.00000			−0.0441942
$513$	−3.25014	+	2.90459i	−0.143497	+	0.128241i
$514$		−	8.28582i		−	0.365472i
$515$	1.73186	−	0.999891i	0.0763149	−	0.0440605i
$516$	1.00296	+	1.73718i	0.0441528	+	0.0764749i
$517$	2.52845	+	0.405477i	0.111201	+	0.0178329i
$518$	−1.74801	−	3.02764i	−0.0768030	−	0.133027i
$519$	−13.8536	−	7.99835i	−0.608104	−	0.351089i
$520$	5.66721			0.248524
$521$		−	25.2556i		−	1.10647i	−0.833026	−	0.553233i	$-0.813394\pi$
$521$		−	25.2556i		−	1.10647i	0.833026	−	0.553233i	$-0.186606\pi$
$522$	−0.766066	+	1.32687i	−0.0335298	+	0.0580753i
$523$	−9.19532	+	15.9268i	−0.402083	+	0.696428i	−0.993977	−	0.109587i	$-0.965047\pi$
$523$	−9.19532	+	15.9268i	−0.402083	+	0.696428i	0.591894	+	0.806016i	$0.298380\pi$
$524$		−	7.20008i		−	0.314537i
$525$	8.59726			0.375215
$526$	12.1077	+	6.99036i	0.527919	+	0.304794i
$527$	1.43949	+	2.49327i	0.0627053	+	0.108609i
$528$	−0.525163	+	3.27478i	−0.0228548	+	0.142517i
$529$	−12.0265	−	20.8304i	−0.522890	−	0.905672i
$530$	26.3417	−	15.2084i	1.14421	−	0.660611i
$531$		−	9.16173i		−	0.397585i
$532$	−1.11152	−	5.32677i	−0.0481904	−	0.230945i
$533$	6.73323			0.291649
$534$	5.76425	+	9.98398i	0.249444	+	0.432049i
$535$	−2.60055	−	4.50428i	−0.112431	−	0.194737i
$536$	−9.86074	−	5.69310i	−0.425919	−	0.245905i
$537$	−5.20486	−	9.01509i	−0.224606	−	0.389030i
$538$	−7.21175	−	4.16371i	−0.310921	−	0.179510i
$539$	6.43515	+	16.8614i	0.277181	+	0.726273i
$540$		−	3.44773i		−	0.148366i
$541$	−15.3902	−	8.88554i	−0.661677	−	0.382019i	0.131239	−	0.991351i	$-0.458105\pi$
$541$	−15.3902	−	8.88554i	−0.661677	−	0.382019i	−0.792916	+	0.609331i	$0.791438\pi$
$542$	25.3510	+	14.6364i	1.08892	+	0.628687i
$543$	−26.2232			−1.12535
$544$			1.09825i			0.0470872i
$545$	10.7333	−	18.5906i	0.459764	−	0.796335i
$546$	1.02600	+	1.77709i	0.0439089	+	0.0760524i
$547$	22.0376	−	38.1702i	0.942259	−	1.63204i	0.181109	−	0.983463i	$-0.442031\pi$
$547$	22.0376	−	38.1702i	0.942259	−	1.63204i	0.761149	−	0.648577i	$-0.224635\pi$
$548$	−1.01202	−	1.75287i	−0.0432313	−	0.0748789i
$549$	−4.04837	+	2.33733i	−0.172780	+	0.0997548i
$550$	−8.14425	−	21.3397i	−0.347272	−	0.909926i
$551$	−6.53760	+	1.36418i	−0.278511	+	0.0581159i
$552$		−	6.85951i		−	0.291960i
$553$	11.2874	−	6.51681i	0.479991	−	0.277123i
$554$	−9.73381	+	5.61982i	−0.413550	+	0.238763i
$555$	4.82763	−	8.36170i	0.204921	−	0.354934i
$556$	−19.1914	+	11.0802i	−0.813896	+	0.469903i
$557$	−21.1776	−	12.2269i	−0.897322	−	0.518069i	−0.0209914	−	0.999780i	$-0.506682\pi$
$557$	−21.1776	−	12.2269i	−0.897322	−	0.518069i	−0.876330	+	0.481711i	$0.840016\pi$
$558$		−	2.62142i		−	0.110974i
$559$		−	3.29724i		−	0.139458i
$560$	3.72739	+	2.15201i	0.157511	+	0.0909391i
$561$	3.59654	+	0.576762i	0.151846	+	0.0243509i
$562$	13.1395			0.554255
$563$	−39.1242			−1.64889			−0.824444	−	0.565943i	$-0.808512\pi$
$563$	−39.1242			−1.64889			−0.824444	+	0.565943i	$0.808512\pi$
$564$	−0.668656	−	0.386049i	−0.0281555	−	0.0162556i
$565$	22.1625	−	12.7955i	0.932385	−	0.538313i
$566$	−12.2273	−	7.05943i	−0.513952	−	0.296730i
$567$	1.08112	−	0.624183i	0.0454026	−	0.0262132i
$568$	1.61897	−	0.934712i	0.0679304	−	0.0392197i
$569$	−18.3969			−0.771236			−0.385618	−	0.922658i	$-0.626012\pi$
$569$	−18.3969			−0.771236			−0.385618	+	0.922658i	$0.626012\pi$
$570$	11.2056	−	10.0142i	0.469350	−	0.419449i
$571$			5.79237i			0.242403i	0.992628	+	0.121202i	$0.0386748\pi$
$571$			5.79237i			0.242403i	−0.992628	+	0.121202i	$0.961325\pi$
$572$	3.43906	−	4.23014i	0.143794	−	0.176871i
$573$	−17.6022	+	10.1627i	−0.735344	+	0.424551i
$574$	4.42853	+	2.55681i	0.184843	+	0.106719i
$575$	23.6201	+	40.9112i	0.985026	+	1.70611i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	3.73753			0.155596			0.0777978	−	0.996969i	$-0.475211\pi$
$577$	3.73753			0.155596			0.0777978	+	0.996969i	$0.475211\pi$
$578$	−15.7938			−0.656937
$579$	−2.41558	−	1.39463i	−0.100388	−	0.0579590i
$580$	2.64119	−	4.57467i	0.109669	−	0.189953i
$581$	−5.32970			−0.221113
$582$	4.01045			0.166239
$583$	4.63314	−	28.8911i	0.191885	−	1.19655i
$584$	4.66802	−	2.69509i	0.193164	−	0.111523i
$585$	−2.83361	+	4.90795i	−0.117155	+	0.202919i
$586$	−12.2851	−	21.2785i	−0.507494	−	0.879006i
$587$	−13.8414	−	23.9740i	−0.571297	−	0.989515i	−0.996433	−	0.0843856i	$-0.973107\pi$
$587$	−13.8414	−	23.9740i	−0.571297	−	0.989515i	0.425137	−	0.905129i	$-0.360226\pi$
$588$		−	5.44158i		−	0.224407i
$589$	8.51997	−	7.61414i	0.351059	−	0.313735i
$590$			31.5871i			1.30042i
$591$	4.03331	+	6.98591i	0.165908	+	0.287362i
$592$	2.42528	−	1.40024i	0.0996784	−	0.0575493i
$593$	3.50513	+	2.02369i	0.143938	+	0.0831028i	0.570240	−	0.821478i	$-0.306850\pi$
$593$	3.50513	+	2.02369i	0.143938	+	0.0831028i	−0.426301	+	0.904581i	$0.640184\pi$
$594$	−2.57346	−	2.09220i	−0.105591	−	0.0858438i
$595$	2.36346	−	4.09362i	0.0968922	−	0.167822i
$596$		−	19.4633i		−	0.797246i
$597$			13.6698i			0.559469i
$598$	−5.63768	+	9.76474i	−0.230542	+	0.399310i
$599$	0.105234	+	0.0607568i	0.00429974	+	0.00248246i	0.502148	−	0.864782i	$-0.332543\pi$
$599$	0.105234	+	0.0607568i	0.00429974	+	0.00248246i	−0.497849	+	0.867264i	$0.665876\pi$
$600$			6.88681i			0.281153i
$601$	−4.24484			−0.173150			−0.0865752	−	0.996245i	$-0.527592\pi$
$601$	−4.24484			−0.173150			−0.0865752	+	0.996245i	$0.527592\pi$
$602$	1.25206	−	2.16863i	0.0510302	−	0.0883868i
$603$	9.86074	−	5.69310i	0.401560	−	0.231841i
$604$	−6.60778	+	11.4450i	−0.268867	+	0.465691i
$605$	−36.0232	−	11.8588i	−1.46455	−	0.482127i
$606$	−0.960091	−	1.66293i	−0.0390010	−	0.0675518i
$607$	−3.93826			−0.159849			−0.0799245	−	0.996801i	$-0.525468\pi$
$607$	−3.93826			−0.159849			−0.0799245	+	0.996801i	$0.525468\pi$
$608$	4.26699	−	0.890378i	0.173049	−	0.0361096i
$609$	1.91266			0.0775050
$610$	13.9577	−	8.05847i	0.565130	−	0.326278i
$611$	0.634569	+	1.09911i	0.0256719	+	0.0444651i
$612$	−0.951116	−	0.549127i	−0.0384466	−	0.0221971i
$613$	−9.09086	+	5.24861i	−0.367176	+	0.211989i	−0.672224	−	0.740348i	$-0.734661\pi$
$613$	−9.09086	+	5.24861i	−0.367176	+	0.211989i	0.305048	+	0.952337i	$0.401328\pi$
$614$	−8.36440	+	14.4876i	−0.337560	+	0.584671i
$615$			14.1228i			0.569484i
$616$	3.86822	−	1.47630i	0.155855	−	0.0594819i
$617$	−3.24205	+	5.61539i	−0.130520	+	0.226067i	−0.923877	−	0.382689i	$-0.874998\pi$
$617$	−3.24205	+	5.61539i	−0.130520	+	0.226067i	0.793357	+	0.608756i	$0.208331\pi$
$618$	−0.290015	+	0.502320i	−0.0116661	+	0.0202063i
$619$	36.5579			1.46939			0.734693	−	0.678399i	$-0.237326\pi$
$619$	36.5579			1.46939			0.734693	+	0.678399i	$0.237326\pi$
$620$			9.03794i			0.362972i
$621$	5.94051	+	3.42976i	0.238385	+	0.137631i
$622$	13.7992	+	23.9010i	0.553299	+	0.958343i
$623$	7.19590	−	12.4637i	0.288298	−	0.499346i
$624$	−1.42353	+	0.821877i	−0.0569869	+	0.0329014i
$625$	6.00295	+	10.3974i	0.240118	+	0.415897i
$626$	−13.0724			−0.522477
$627$	−0.674929	−	14.4411i	−0.0269541	−	0.576721i
$628$	−10.5408			−0.420622
$629$	−1.53781	−	2.66357i	−0.0613167	−	0.106204i
$630$	−3.72739	+	2.15201i	−0.148503	+	0.0857382i
$631$	−17.1183	+	29.6498i	−0.681469	+	1.18034i	0.293064	+	0.956093i	$0.405325\pi$
$631$	−17.1183	+	29.6498i	−0.681469	+	1.18034i	−0.974533	+	0.224245i	$0.928008\pi$
$632$	5.22027	+	9.04178i	0.207651	+	0.359663i
$633$	16.7208	+	9.65373i	0.664590	+	0.383701i
$634$		−	29.1700i		−	1.15849i
$635$	39.7769			1.57850
$636$	−4.41114	+	7.64033i	−0.174913	+	0.302959i
$637$	−4.47231	+	7.74627i	−0.177199	+	0.306918i
$638$	−1.81188	−	4.74751i	−0.0717330	−	0.187956i
$639$			1.86942i			0.0739533i
$640$	−1.72386	+	2.98582i	−0.0681417	+	0.118025i
$641$	24.1665	−	13.9525i	0.954518	−	0.551091i	0.0600363	−	0.998196i	$-0.480878\pi$
$641$	24.1665	−	13.9525i	0.954518	−	0.551091i	0.894481	+	0.447105i	$0.147545\pi$
$642$	1.30645	+	0.754278i	0.0515614	+	0.0297690i
$643$	−20.3499	−	35.2471i	−0.802523	−	1.39001i	−0.917951	−	0.396694i	$-0.870157\pi$
$643$	−20.3499	−	35.2471i	−0.802523	−	1.39001i	0.115428	−	0.993316i	$-0.463176\pi$
$644$	−7.41594	+	4.28159i	−0.292229	+	0.168718i
$645$	6.91585			0.272311
$646$	−0.977861	−	4.68624i	−0.0384734	−	0.184378i
$647$	15.7172			0.617907			0.308953	−	0.951077i	$-0.400021\pi$
$647$	15.7172			0.617907			0.308953	+	0.951077i	$0.400021\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	23.5774	+	19.1681i	0.925493	+	0.752415i
$650$	5.66011	−	9.80360i	0.222008	−	0.384529i
$651$	−2.83406	+	1.63625i	−0.111076	+	0.0641296i
$652$	−0.584496	+	1.01238i	−0.0228906	+	0.0396477i
$653$	16.5807			0.648855			0.324427	−	0.945911i	$-0.394828\pi$
$653$	16.5807			0.648855			0.324427	+	0.945911i	$0.394828\pi$
$654$			6.22631i			0.243468i
$655$	−21.4981	−	12.4120i	−0.840002	−	0.484975i
$656$	−2.04813	+	3.54746i	−0.0799659	+	0.138505i
$657$			5.39017i			0.210291i
$658$			0.963861i			0.0375752i
$659$	19.8485	−	34.3787i	0.773189	−	1.33920i	−0.162618	−	0.986689i	$-0.551994\pi$
$659$	19.8485	−	34.3787i	0.773189	−	1.33920i	0.935807	−	0.352513i	$-0.114673\pi$
$660$	8.87260	+	7.21332i	0.345365	+	0.280778i
$661$	−8.00302	−	4.62055i	−0.311281	−	0.179718i	0.336218	−	0.941784i	$-0.390852\pi$
$661$	−8.00302	−	4.62055i	−0.311281	−	0.179718i	−0.647500	+	0.762066i	$0.724185\pi$
$662$	21.3396	−	12.3204i	0.829388	−	0.478847i
$663$	0.902630	+	1.56340i	0.0350552	+	0.0607174i
$664$		−	4.26934i		−	0.165683i
$665$	−17.8209	−	5.86383i	−0.691064	−	0.227390i
$666$			2.80047i			0.108516i
$667$	5.25484	+	9.10165i	0.203468	+	0.352417i
$668$	−3.26312	−	5.65190i	−0.126254	−	0.218678i
$669$	3.16855	−	5.48809i	0.122503	−	0.212182i
$670$	−33.9971	+	19.6282i	−1.31342	+	0.758305i
$671$	2.45496	−	15.3085i	0.0947725	−	0.590978i
$672$	−1.24837			−0.0481568
$673$	4.15137			0.160023			0.0800117	−	0.996794i	$-0.474504\pi$
$673$	4.15137			0.160023			0.0800117	+	0.996794i	$0.474504\pi$
$674$	−6.43400	+	11.1440i	−0.247828	+	0.429251i
$675$	−5.96415	−	3.44340i	−0.229560	−	0.132537i
$676$	−10.2981			−0.396080
$677$	26.3131			1.01129			0.505647	−	0.862740i	$-0.331254\pi$
$677$	26.3131			1.01129			0.505647	+	0.862740i	$0.331254\pi$
$678$	−3.71130	+	6.42816i	−0.142532	+	0.246872i
$679$	−2.50326	−	4.33577i	−0.0960662	−	0.166392i
$680$	3.27919	+	1.89324i	0.125751	+	0.0726024i
$681$	−15.1223	+	8.73084i	−0.579486	+	0.334566i
$682$	6.74613	+	5.48453i	0.258323	+	0.210013i
$683$		−	43.3727i		−	1.65961i	−0.558053	−	0.829806i	$-0.688451\pi$
$683$		−	43.3727i		−	1.65961i	0.558053	−	0.829806i	$-0.311549\pi$
$684$	−1.36241	+	4.14051i	−0.0520929	+	0.158316i
$685$	−6.97833			−0.266628
$686$	−13.4508	+	7.76582i	−0.513554	+	0.296501i
$687$	−22.7550	+	13.1376i	−0.868158	+	0.501232i
$688$	1.73718	+	1.00296i	0.0662292	+	0.0382374i
$689$	12.5588	−	7.25084i	0.478453	−	0.276235i
$690$	−20.4813	−	11.8249i	−0.779708	−	0.450165i
$691$	26.5642			1.01055			0.505275	−	0.862958i	$-0.331391\pi$
$691$	26.5642			1.01055			0.505275	+	0.862958i	$0.331391\pi$
$692$	−15.9967			−0.608104
$693$	−0.655595	+	4.08813i	−0.0249040	+	0.155295i
$694$	−24.8878	−	14.3690i	−0.944729	−	0.545440i
$695$			76.4026i			2.89812i
$696$			1.53213i			0.0580753i
$697$	3.89601	+	2.24936i	0.147572	+	0.0852007i
$698$	−11.8601	+	6.84744i	−0.448912	+	0.259179i
$699$	−3.98847	+	6.90824i	−0.150858	+	0.261294i
$700$	7.44545	−	4.29863i	0.281411	−	0.162473i
$701$	0.725834	−	0.419060i	0.0274144	−	0.0158277i	−0.486230	−	0.873831i	$-0.661628\pi$
$701$	0.725834	−	0.419060i	0.0274144	−	0.0158277i	0.513645	+	0.858003i	$0.328295\pi$
$702$		−	1.64375i		−	0.0620395i
$703$	−9.10191	+	8.13421i	−0.343285	+	0.306788i
$704$	1.18259	+	3.09863i	0.0445704	+	0.116784i
$705$	−2.30534	+	1.33099i	−0.0868242	+	0.0501280i
$706$	−7.11038	−	12.3155i	−0.267603	−	0.463502i
$707$	−1.19855	+	2.07594i	−0.0450759	+	0.0780738i
$708$	−4.58086	−	7.93429i	−0.172159	−	0.298189i
$709$	−4.24072	+	7.34515i	−0.159264	+	0.275853i	−0.934603	−	0.355692i	$-0.884245\pi$
$709$	−4.24072	+	7.34515i	−0.159264	+	0.275853i	0.775340	+	0.631544i	$0.217579\pi$
$710$		−	6.44526i		−	0.241886i
$711$	−10.4405			−0.391551
$712$	9.98398	+	5.76425i	0.374165	+	0.216025i
$713$	−15.5726	−	8.99084i	−0.583198	−	0.336709i
$714$			1.37102i			0.0513092i
$715$	−6.70197	−	17.5606i	−0.250640	−	0.656728i
$716$	−9.01509	−	5.20486i	−0.336910	−	0.194515i
$717$	−2.10829	−	3.65166i	−0.0787355	−	0.136374i
$718$	−15.7117	−	9.07113i	−0.586354	−	0.338532i
$719$	−11.8398	−	20.5072i	−0.441550	−	0.764788i	0.556254	−	0.831012i	$-0.312238\pi$
$719$	−11.8398	−	20.5072i	−0.441550	−	0.764788i	−0.997805	+	0.0662244i	$0.978905\pi$
$720$	−1.72386	−	2.98582i	−0.0642446	−	0.111275i
$721$	0.724089			0.0269665
$722$	−17.4145	+	7.59847i	−0.648099	+	0.282786i
$723$			27.5881i			1.02601i
$724$	−22.7100	+	13.1116i	−0.844010	+	0.487290i
$725$	−5.27575	−	9.13787i	−0.195937	−	0.339372i
$726$	10.7684	−	2.24543i	0.399652	−	0.0833359i
$727$	−3.51442	−	6.08716i	−0.130343	−	0.225760i	0.793466	−	0.608615i	$-0.208274\pi$
$727$	−3.51442	−	6.08716i	−0.130343	−	0.225760i	−0.923809	+	0.382854i	$0.874941\pi$
$728$	1.77709	+	1.02600i	0.0658634	+	0.0380262i
$729$	−1.00000			−0.0370370
$730$		−	18.5838i		−	0.687818i
$731$	1.10150	−	1.90786i	0.0407406	−	0.0705647i
$732$	−2.33733	+	4.04837i	−0.0863902	+	0.149632i
$733$			6.89916i			0.254826i	0.991850	+	0.127413i	$0.0406674\pi$
$733$			6.89916i			0.254826i	−0.991850	+	0.127413i	$0.959333\pi$
$734$	4.96888			0.183405
$735$	−16.2476	−	9.38054i	−0.599301	−	0.346006i
$736$	−3.42976	−	5.94051i	−0.126423	−	0.218970i
$737$	−5.97961	+	37.2873i	−0.220262	+	1.37350i
$738$	−2.04813	−	3.54746i	−0.0753926	−	0.130584i
$739$	−25.3482	+	14.6348i	−0.932449	+	0.538350i	−0.887585	−	0.460644i	$-0.847619\pi$
$739$	−25.3482	+	14.6348i	−0.932449	+	0.538350i	−0.0448635	+	0.998993i	$0.514285\pi$
$740$		−	9.65526i		−	0.354934i
$741$	5.34242	−	4.77443i	0.196259	−	0.175393i
$742$	11.0134			0.404316
$743$	−9.05408	−	15.6821i	−0.332162	−	0.575321i	0.650774	−	0.759272i	$-0.274445\pi$
$743$	−9.05408	−	15.6821i	−0.332162	−	0.575321i	−0.982935	+	0.183951i	$0.941111\pi$
$744$	−1.31071	−	2.27022i	−0.0480530	−	0.0832302i
$745$	−58.1137	−	33.5520i	−2.12912	−	1.22925i
$746$	15.1273	+	26.2013i	0.553851	+	0.959299i
$747$	3.69736	+	2.13467i	0.135279	+	0.0781035i
$748$	3.40308	−	1.29878i	0.124429	−	0.0474881i
$749$		−	1.88323i		−	0.0688118i
$750$	5.63367	+	3.25260i	0.205713	+	0.118768i
$751$	−31.6845	−	18.2930i	−1.15618	−	0.667523i	−0.205797	−	0.978595i	$-0.565979\pi$
$751$	−31.6845	−	18.2930i	−1.15618	−	0.667523i	−0.950386	+	0.311072i	$0.899312\pi$
$752$	−0.772098			−0.0281555
$753$		−	2.82317i		−	0.102882i
$754$	1.25922	−	2.18104i	0.0458583	−	0.0794288i
$755$	22.7818	+	39.4592i	0.829115	+	1.43607i
$756$	0.624183	−	1.08112i	0.0227013	−	0.0393198i
$757$	16.0264	+	27.7586i	0.582491	+	1.00890i	0.995183	+	0.0980330i	$0.0312551\pi$
$757$	16.0264	+	27.7586i	0.582491	+	1.00890i	−0.412693	+	0.910870i	$0.635412\pi$
$758$	−19.9948	+	11.5440i	−0.726244	+	0.419297i
$759$	−21.2551	+	8.11197i	−0.771510	+	0.294446i
$760$	4.69720	−	14.2754i	0.170385	−	0.517821i
$761$		−	41.8466i		−	1.51694i	−0.651708	−	0.758470i	$-0.725947\pi$
$761$		−	41.8466i		−	1.51694i	0.651708	−	0.758470i	$-0.274053\pi$
$762$	−9.99146	+	5.76857i	−0.361953	+	0.208973i
$763$	6.73137	−	3.88636i	0.243692	−	0.140696i
$764$	−10.1627	+	17.6022i	−0.367672	+	0.636827i
$765$	−3.27919	+	1.89324i	−0.118559	+	0.0684502i
$766$	4.34845	+	2.51058i	0.157116	+	0.0907110i
$767$			15.0596i			0.543772i
$768$		−	1.00000i		−	0.0360844i
$769$	−10.0853	−	5.82275i	−0.363685	−	0.209974i	0.307011	−	0.951706i	$-0.400671\pi$
$769$	−10.0853	−	5.82275i	−0.363685	−	0.209974i	−0.670696	+	0.741732i	$0.734004\pi$
$770$	2.26031	−	14.0947i	0.0814560	−	0.507939i
$771$	8.28582			0.298406
$772$	−2.78927			−0.100388
$773$	−5.63424	−	3.25293i	−0.202650	−	0.117000i	0.395241	−	0.918577i	$-0.370661\pi$
$773$	−5.63424	−	3.25293i	−0.202650	−	0.117000i	−0.597891	+	0.801578i	$0.703994\pi$
$774$	−1.73718	+	1.00296i	−0.0624415	+	0.0360506i
$775$	15.6346	+	9.02661i	0.561610	+	0.324246i
$776$	3.47315	−	2.00523i	0.124679	−	0.0719834i
$777$	3.02764	−	1.74801i	0.108616	−	0.0627094i
$778$	12.3702			0.443494
$779$	5.58076	−	16.9606i	0.199951	−	0.607676i
$780$			5.66721i			0.202919i
$781$	−4.81090	−	3.91120i	−0.172147	−	0.139954i
$782$	−6.52419	+	3.76674i	−0.233305	+	0.134698i
$783$	−1.32687	−	0.766066i	−0.0474183	−	0.0273770i
$784$	−2.72079	−	4.71255i	−0.0971711	−	0.168305i
$785$	−18.1708	+	31.4728i	−0.648544	+	1.12331i
$786$	7.20008			0.256818
$787$	−9.94951			−0.354662			−0.177331	−	0.984151i	$-0.556746\pi$
$787$	−9.94951			−0.354662			−0.177331	+	0.984151i	$0.556746\pi$
$788$	6.98591	+	4.03331i	0.248863	+	0.143681i
$789$	−6.99036	+	12.1077i	−0.248863	+	0.431044i
$790$	35.9961			1.28068
$791$	9.26613			0.329466
$792$	−3.27478	−	0.525163i	−0.116364	−	0.0186608i
$793$	6.65453	−	3.84199i	0.236309	−	0.136433i
$794$	8.99311	−	15.5765i	0.319154	−	0.552790i
$795$	15.2084	+	26.3417i	0.539387	+	0.934245i
$796$	6.83492	+	11.8384i	0.242257	+	0.419602i
$797$		−	9.61068i		−	0.340428i	−0.985407	−	0.170214i	$-0.945554\pi$
$797$		−	9.61068i		−	0.340428i	0.985407	−	0.170214i	$-0.0544458\pi$
$798$	5.32677	−	1.11152i	0.188566	−	0.0393473i
$799$			0.847959i			0.0299986i
$800$	3.44340	+	5.96415i	0.121743	+	0.210865i
$801$	−9.98398	+	5.76425i	−0.352767	+	0.203670i
$802$	−22.0003	−	12.7019i	−0.776859	−	0.448520i
$803$	−13.8714	−	11.2773i	−0.489511	−	0.397967i
$804$	5.69310	−	9.86074i	0.200780	−	0.347761i
$805$			29.5235i			1.04057i
$806$			4.30897i			0.151777i
$807$	4.16371	−	7.21175i	0.146569	−	0.253866i
$808$	−1.66293	−	0.960091i	−0.0585016	−	0.0337759i
$809$			8.16091i			0.286922i	0.989656	+	0.143461i	$0.0458232\pi$
$809$			8.16091i			0.286922i	−0.989656	+	0.143461i	$0.954177\pi$
$810$	3.44773			0.121141
$811$	−17.0726	+	29.5706i	−0.599499	+	1.03836i	0.393396	+	0.919369i	$0.371300\pi$
$811$	−17.0726	+	29.5706i	−0.599499	+	1.03836i	−0.992895	+	0.118994i	$0.962033\pi$
$812$	1.65641	−	0.956331i	0.0581287	−	0.0335606i
$813$	−14.6364	+	25.3510i	−0.513321	+	0.889097i
$814$	−7.20691	−	5.85913i	−0.252602	−	0.205363i
$815$	2.01518	+	3.49039i	0.0705887	+	0.122263i
$816$	−1.09825			−0.0384466
$817$	−8.30553	−	2.73288i	−0.290574	−	0.0956112i
$818$	−12.0672			−0.421919
$819$	−1.77709	+	1.02600i	−0.0620966	+	0.0358515i
$820$	7.06138	+	12.2307i	0.246594	+	0.427113i
$821$	−42.9779	−	24.8133i	−1.49994	−	0.865989i	−0.499938	−	0.866061i	$-0.666644\pi$
$821$	−42.9779	−	24.8133i	−1.49994	−	0.865989i	−1.00000		7.20238e-5i	$0.999977\pi$
$822$	1.75287	−	1.01202i	0.0611383	−	0.0352982i
$823$	4.14575	−	7.18064i	0.144512	−	0.250301i	−0.784679	−	0.619902i	$-0.787172\pi$
$823$	4.14575	−	7.18064i	0.144512	−	0.250301i	0.929191	+	0.369601i	$0.120506\pi$
$824$			0.580029i			0.0202063i
$825$	21.3397	−	8.14425i	0.742951	−	0.283547i
$826$	−5.71860	+	9.90490i	−0.198975	+	0.344636i
$827$	24.1393	−	41.8105i	0.839406	−	1.45389i	−0.0509868	−	0.998699i	$-0.516237\pi$
$827$	24.1393	−	41.8105i	0.839406	−	1.45389i	0.890392	−	0.455194i	$-0.150430\pi$
$828$	6.85951			0.238385
$829$		−	27.0954i		−	0.941063i	−0.882383	−	0.470532i	$-0.844062\pi$
$829$		−	27.0954i		−	0.941063i	0.882383	−	0.470532i	$-0.155938\pi$
$830$	−12.7475	−	7.35976i	−0.442471	−	0.255461i
$831$	−5.61982	−	9.73381i	−0.194949	−	0.337662i
$832$	−0.821877	+	1.42353i	−0.0284935	+	0.0493521i
$833$	−5.17557	+	2.98812i	−0.179323	+	0.103532i
$834$	−11.0802	−	19.1914i	−0.383674	−	0.664543i
$835$	−22.5007			−0.778669
$836$	−7.80504	−	12.1689i	−0.269943	−	0.420869i
$837$	2.62142			0.0906096
$838$	−6.56926	−	11.3783i	−0.226931	−	0.393057i
$839$	23.8871	−	13.7912i	0.824674	−	0.476126i	−0.0273515	−	0.999626i	$-0.508707\pi$
$839$	23.8871	−	13.7912i	0.824674	−	0.476126i	0.852026	+	0.523500i	$0.175374\pi$
$840$	−2.15201	+	3.72739i	−0.0742515	+	0.128607i
$841$	13.3263	+	23.0818i	0.459527	+	0.795924i
$842$	−2.50186	−	1.44445i	−0.0862198	−	0.0497790i
$843$			13.1395i			0.452548i
$844$	19.3075			0.664590
$845$	−17.7525	+	30.7482i	−0.610703	+	1.05777i
$846$	0.386049	−	0.668656i	0.0132726	−	0.0229889i
$847$	−9.14902	−	10.2403i	−0.314364	−	0.351861i
$848$			8.82229i			0.302959i
$849$	7.05943	−	12.2273i	0.242279	−	0.419640i
$850$	6.55015	−	3.78173i	0.224668	−	0.129712i
$851$	16.6362	+	9.60494i	0.570283	+	0.329253i
$852$	0.934712	+	1.61897i	0.0320227	+	0.0554650i
$853$	38.2447	−	22.0806i	1.30948	−	0.756026i	0.327467	−	0.944863i	$-0.393805\pi$
$853$	38.2447	−	22.0806i	1.30948	−	0.756026i	0.982008	+	0.188837i	$0.0604718\pi$
$854$	5.83568			0.199693
$855$	10.0142	+	11.2056i	0.342479	+	0.383223i
$856$	1.50856			0.0515614
$857$	13.7485	+	23.8132i	0.469641	+	0.813443i	0.999398	−	0.0347074i	$-0.0110499\pi$
$857$	13.7485	+	23.8132i	0.469641	+	0.813443i	−0.529756	+	0.848150i	$0.677717\pi$
$858$	4.23014	+	3.43906i	0.144415	+	0.117407i
$859$	−27.7978	+	48.1471i	−0.948447	+	1.64276i	−0.199750	+	0.979847i	$0.564013\pi$
$859$	−27.7978	+	48.1471i	−0.948447	+	1.64276i	−0.748698	+	0.662912i	$0.769320\pi$
$860$	5.98930	−	3.45793i	0.204234	−	0.117914i
$861$	−2.55681	+	4.42853i	−0.0871359	+	0.150924i
$862$	2.43772			0.0830289
$863$			44.3053i			1.50817i	0.656778	+	0.754084i	$0.271919\pi$
$863$			44.3053i			1.50817i	−0.656778	+	0.754084i	$0.728081\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	−27.5761	+	47.7632i	−0.937616	+	1.62400i
$866$		−	33.4176i		−	1.13558i
$867$		−	15.7938i		−	0.536387i
$868$	−1.63625	+	2.83406i	−0.0555378	+	0.0961943i
$869$	21.8437	−	26.8684i	0.740996	−	0.911447i
$870$	4.57467	+	2.64119i	0.155096	+	0.0895446i
$871$	−16.2086	+	9.35806i	−0.549209	+	0.317086i
$872$	3.11316	+	5.39214i	0.105425	+	0.182601i
$873$			4.01045i			0.135733i
$874$	19.9241	+	22.2943i	0.673941	+	0.754118i
$875$		−	8.12087i		−	0.274536i
$876$	2.69509	+	4.66802i	0.0910585	+	0.157718i
$877$	−4.48687	−	7.77149i	−0.151511	−	0.262425i	0.780272	−	0.625440i	$-0.215081\pi$
$877$	−4.48687	−	7.77149i	−0.151511	−	0.262425i	−0.931783	+	0.363015i	$0.881747\pi$
$878$	−7.04233	+	12.1977i	−0.237667	+	0.411652i
$879$	21.2785	−	12.2851i	0.717705	−	0.414367i
$880$	11.2906	+	1.81062i	0.380604	+	0.0610359i
$881$	22.9197			0.772184			0.386092	−	0.922460i	$-0.373825\pi$
$881$	22.9197			0.772184			0.386092	+	0.922460i	$0.373825\pi$
$882$	5.44158			0.183228
$883$	−24.1800	+	41.8810i	−0.813723	+	1.40941i	0.0965185	+	0.995331i	$0.469229\pi$
$883$	−24.1800	+	41.8810i	−0.813723	+	1.40941i	−0.910241	+	0.414078i	$0.864104\pi$
$884$	1.56340	+	0.902630i	0.0525829	+	0.0303587i
$885$	−31.5871			−1.06179
$886$	3.60383			0.121073
$887$	2.18991	−	3.79304i	0.0735301	−	0.127358i	−0.826916	−	0.562325i	$-0.809907\pi$
$887$	2.18991	−	3.79304i	0.0735301	−	0.127358i	0.900446	+	0.434968i	$0.143240\pi$
$888$	1.40024	+	2.42528i	0.0469888	+	0.0813870i
$889$	12.4730	+	7.20129i	0.418331	+	0.241524i
$890$	34.4220	−	19.8736i	1.15383	−	0.666163i
$891$	2.09220	−	2.57346i	0.0700912	−	0.0862143i
$892$		−	6.33710i		−	0.212182i
$893$	3.29454	−	0.687459i	0.110247	−	0.0230049i
$894$	19.4633			0.650949
$895$	−31.0816	+	17.9449i	−1.03894	+	0.599833i
$896$	−1.08112	+	0.624183i	−0.0361176	+	0.0208525i
$897$	−9.76474	−	5.63768i	−0.326035	−	0.188237i
$898$	−8.49717	+	4.90584i	−0.283554	+	0.163710i
$899$	3.47827	+	2.00818i	0.116007	+	0.0669766i
$900$	−6.88681			−0.229560
$901$	9.68911			0.322791
$902$	13.4143	+	2.15120i	0.446649	+	0.0716271i
$903$	2.16863	+	1.25206i	0.0721675	+	0.0416659i
$904$			7.42260i			0.246872i
$905$			90.4105i			3.00535i
$906$	−11.4450	−	6.60778i	−0.380235	−	0.219529i
$907$	8.60259	−	4.96671i	0.285644	−	0.164917i	−0.350332	−	0.936626i	$-0.613931\pi$
$907$	8.60259	−	4.96671i	0.285644	−	0.164917i	0.635976	+	0.771709i	$0.280598\pi$
$908$	−8.73084	+	15.1223i	−0.289743	+	0.501850i
$909$	1.66293	−	0.960091i	0.0551558	−	0.0318442i
$910$	6.12692	−	3.53738i	0.203105	−	0.117263i
$911$		−	0.535193i		−	0.0177317i	−0.999961	−	0.00886587i	$-0.997178\pi$
$911$		−	0.535193i		−	0.0177317i	0.999961	−	0.00886587i	$-0.00282213\pi$
$912$	0.890378	+	4.26699i	0.0294834	+	0.141294i
$913$	−13.2291	+	5.04887i	−0.437819	+	0.167093i
$914$	27.9529	−	16.1386i	0.924599	−	0.533818i
$915$	8.05847	+	13.9577i	0.266405	+	0.461427i
$916$	−13.1376	+	22.7550i	−0.434079	+	0.751847i
$917$	−4.49417	−	7.78413i	−0.148411	−	0.257055i
$918$	0.549127	−	0.951116i	0.0181239	−	0.0313915i
$919$		−	36.7107i		−	1.21097i	−0.795855	−	0.605487i	$-0.792978\pi$
$919$		−	36.7107i		−	1.21097i	0.795855	−	0.605487i	$-0.207022\pi$
$920$	−23.6497			−0.779708
$921$	−14.4876	−	8.36440i	−0.477381	−	0.275616i
$922$	15.8758	+	9.16591i	0.522842	+	0.301863i
$923$		−	3.07287i		−	0.101145i
$924$	1.47630	+	3.86822i	0.0485668	+	0.127255i
$925$	−16.7024	−	9.64316i	−0.549173	−	0.317065i
$926$	−17.9598	−	31.1073i	−0.590196	−	1.02225i
$927$	−0.502320	−	0.290015i	−0.0164984	−	0.00952533i
$928$	0.766066	+	1.32687i	0.0251474	+	0.0435565i
$929$	15.4136	+	26.6972i	0.505705	+	0.875907i	0.999978	+	0.00660005i	$0.00210088\pi$
$929$	15.4136	+	26.6972i	0.505705	+	0.875907i	−0.494273	+	0.869307i	$0.664566\pi$
$930$	−9.03794			−0.296366
$931$	15.8055	+	17.6859i	0.518006	+	0.579631i
$932$			7.97695i			0.261294i
$933$	−23.9010	+	13.7992i	−0.782484	+	0.451767i
$934$	−15.6257	−	27.0645i	−0.511288	−	0.885577i
$935$	1.98852	−	12.3999i	0.0650315	−	0.405520i
$936$	−0.821877	−	1.42353i	−0.0268639	−	0.0465296i
$937$	32.2242	+	18.6047i	1.05272	+	0.607788i	0.923410	−	0.383816i	$-0.125390\pi$
$937$	32.2242	+	18.6047i	1.05272	+	0.607788i	0.129311	+	0.991604i	$0.458724\pi$
$938$	−14.2141			−0.464108
$939$		−	13.0724i		−	0.426601i
$940$	−1.33099	+	2.30534i	−0.0434121	+	0.0751920i
$941$	12.9510	−	22.4318i	0.422191	−	0.731257i	−0.573962	−	0.818882i	$-0.694594\pi$
$941$	12.9510	−	22.4318i	0.422191	−	0.731257i	0.996154	+	0.0876248i	$0.0279277\pi$
$942$		−	10.5408i		−	0.343437i
$943$	−28.0983			−0.915007
$944$	−7.93429	−	4.58086i	−0.258239	−	0.149094i
$945$	−2.15201	−	3.72739i	−0.0700049	−	0.121252i
$946$	1.05343	−	6.56895i	0.0342501	−	0.213575i
$947$	−22.8650	−	39.6033i	−0.743012	−	1.28694i	−0.951118	−	0.308829i	$-0.900063\pi$
$947$	−22.8650	−	39.6033i	−0.743012	−	1.28694i	0.208105	−	0.978106i	$-0.433270\pi$
$948$	−9.04178	+	5.22027i	−0.293663	+	0.169547i
$949$		−	8.86012i		−	0.287612i
$950$	−20.0033	−	22.3831i	−0.648994	−	0.726202i
$951$	29.1700			0.945903
$952$	0.685511	+	1.18734i	0.0222176	+	0.0384819i
$953$	−22.6280	−	39.1929i	−0.732994	−	1.26958i	−0.955598	−	0.294673i	$-0.904789\pi$
$953$	−22.6280	−	39.1929i	−0.732994	−	1.26958i	0.222604	−	0.974909i	$-0.428544\pi$
$954$	−7.64033	−	4.41114i	−0.247365	−	0.142816i
$955$	35.0381	+	60.6877i	1.13381	+	1.96381i
$956$	−3.65166	−	2.10829i	−0.118103	−	0.0681870i
$957$	4.74751	−	1.81188i	0.153465	−	0.0585698i
$958$			25.4355i			0.821783i
$959$	−2.18822	−	1.26337i	−0.0706614	−	0.0407964i
$960$	−2.98582	−	1.72386i	−0.0963669	−	0.0556374i
$961$	24.1282			0.778327
$962$		−	4.60329i		−	0.148416i
$963$	−0.754278	+	1.30645i	−0.0243063	+	0.0420997i
$964$	13.7940	+	23.8920i	0.444276	+	0.769509i
$965$	−4.80832	+	8.32825i	−0.154785	+	0.268096i
$966$	−4.28159	−	7.41594i	−0.137758	−	0.238604i
$967$	7.56019	−	4.36488i	0.243119	−	0.140365i	−0.373490	−	0.927634i	$-0.621839\pi$
$967$	7.56019	−	4.36488i	0.243119	−	0.140365i	0.616610	+	0.787269i	$0.288506\pi$
$968$	8.20297	−	7.32879i	0.263654	−	0.235556i
$969$	4.68624	−	0.977861i	0.150544	−	0.0314134i
$970$		−	13.8269i		−	0.443956i
$971$	38.5598	−	22.2625i	1.23744	−	0.714438i	0.268873	−	0.963176i	$-0.413349\pi$
$971$	38.5598	−	22.2625i	1.23744	−	0.714438i	0.968571	+	0.248737i	$0.0800156\pi$
$972$	−0.866025	+	0.500000i	−0.0277778	+	0.0160375i
$973$	−13.8321	+	23.9579i	−0.443436	+	0.768054i
$974$	−18.6483	+	10.7666i	−0.597531	+	0.344985i
$975$	9.80360	+	5.66011i	0.313966	+	0.181269i
$976$			4.67466i			0.149632i
$977$			28.9256i			0.925412i	0.886512	+	0.462706i	$0.153121\pi$
$977$			28.9256i			0.925412i	−0.886512	+	0.462706i	$0.846879\pi$
$978$	−1.01238	−	0.584496i	−0.0323722	−	0.0186901i
$979$	6.05434	−	37.7534i	0.193498	−	1.20660i
$980$	−18.7611			−0.599301
$981$	−6.22631			−0.198791
$982$	18.0097	+	10.3979i	0.574714	+	0.331811i
$983$	52.0382	−	30.0443i	1.65976	−	0.958264i	0.686939	−	0.726715i	$-0.258954\pi$
$983$	52.0382	−	30.0443i	1.65976	−	0.958264i	0.972823	−	0.231549i	$-0.0743794\pi$
$984$	−3.54746	−	2.04813i	−0.113089	−	0.0652919i
$985$	24.0855	−	13.9058i	0.767427	−	0.443074i
$986$	1.45724	−	0.841335i	0.0464078	−	0.0267936i
$987$	−0.963861			−0.0306800
$988$	2.23946	−	6.80599i	0.0712468	−	0.216527i
$989$			13.7596i			0.437530i
$990$	−7.21332	+	8.87260i	−0.229254	+	0.281990i
$991$	26.6189	−	15.3685i	0.845578	−	0.488195i	−0.0135780	−	0.999908i	$-0.504322\pi$
$991$	26.6189	−	15.3685i	0.845578	−	0.488195i	0.859157	+	0.511713i	$0.170989\pi$
$992$	−2.27022	−	1.31071i	−0.0720795	−	0.0416151i
$993$	12.3204	+	21.3396i	0.390977	+	0.677192i
$994$	1.16686	−	2.02107i	0.0370107	−	0.0641043i
$995$	47.1298			1.49412
$996$	4.26934			0.135279
$997$	−36.7710	−	21.2298i	−1.16455	−	0.672354i	−0.212160	−	0.977235i	$-0.568050\pi$
$997$	−36.7710	−	21.2298i	−1.16455	−	0.672354i	−0.952390	+	0.304881i	$0.901383\pi$
$998$	−6.60058	+	11.4325i	−0.208938	+	0.361891i
$999$	−2.80047			−0.0886030

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1254.2.k.b.373.1	yes	40
11.10	odd	2		1254.2.k.a.373.1	✓	40
19.8	odd	6		1254.2.k.a.901.1	yes	40
209.65	even	6	inner	1254.2.k.b.901.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1254.2.k.a.373.1	✓	40	11.10	odd	2
1254.2.k.a.901.1	yes	40	19.8	odd	6
1254.2.k.b.373.1	yes	40	1.1	even	1	trivial
1254.2.k.b.901.1	yes	40	209.65	even	6	inner

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:	\( N \)	\(=\)	\( 1254 = 2 \cdot 3 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1254.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.72386 + 2.98582i) q^{5} +(-0.866025 - 0.500000i) q^{6} +1.24837i q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.72386 + 2.98582i) q^{10} +(1.18259 + 3.09863i) q^{11} -1.00000i q^{12} +(-0.821877 + 1.42353i) q^{13} +(-1.08112 + 0.624183i) q^{14} +(-2.98582 - 1.72386i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.951116 + 0.549127i) q^{17} +1.00000 q^{18} +(2.90459 + 3.25014i) q^{19} -3.44773 q^{20} +(-0.624183 - 1.08112i) q^{21} +(-2.09220 + 2.57346i) q^{22} +(3.42976 - 5.94051i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-3.44340 + 5.96415i) q^{25} -1.64375 q^{26} +1.00000i q^{27} +(-1.08112 - 0.624183i) q^{28} +(-0.766066 + 1.32687i) q^{29} -3.44773i q^{30} -2.62142i q^{31} +(0.500000 - 0.866025i) q^{32} +(-2.57346 - 2.09220i) q^{33} +(-0.951116 - 0.549127i) q^{34} +(-3.72739 + 2.15201i) q^{35} +(0.500000 + 0.866025i) q^{36} +2.80047i q^{37} +(-1.36241 + 4.14051i) q^{38} -1.64375i q^{39} +(-1.72386 - 2.98582i) q^{40} +(-2.04813 - 3.54746i) q^{41} +(0.624183 - 1.08112i) q^{42} +(-1.73718 + 1.00296i) q^{43} +(-3.27478 - 0.525163i) q^{44} +3.44773 q^{45} +6.85951 q^{46} +(0.386049 - 0.668656i) q^{47} +(0.866025 + 0.500000i) q^{48} +5.44158 q^{49} -6.88681 q^{50} +(0.549127 - 0.951116i) q^{51} +(-0.821877 - 1.42353i) q^{52} +(-7.64033 - 4.41114i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-7.21332 + 8.87260i) q^{55} -1.24837i q^{56} +(-4.14051 - 1.36241i) q^{57} -1.53213 q^{58} +(7.93429 - 4.58086i) q^{59} +(2.98582 - 1.72386i) q^{60} +(-4.04837 - 2.33733i) q^{61} +(2.27022 - 1.31071i) q^{62} +(1.08112 + 0.624183i) q^{63} +1.00000 q^{64} -5.66721 q^{65} +(0.525163 - 3.27478i) q^{66} +(9.86074 + 5.69310i) q^{67} -1.09825i q^{68} +6.85951i q^{69} +(-3.72739 - 2.15201i) q^{70} +(-1.61897 + 0.934712i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-4.66802 + 2.69509i) q^{73} +(-2.42528 + 1.40024i) q^{74} -6.88681i q^{75} +(-4.26699 + 0.890378i) q^{76} +(-3.86822 + 1.47630i) q^{77} +(1.42353 - 0.821877i) q^{78} +(-5.22027 - 9.04178i) q^{79} +(1.72386 - 2.98582i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.04813 - 3.54746i) q^{82} +4.26934i q^{83} +1.24837 q^{84} +(-3.27919 - 1.89324i) q^{85} +(-1.73718 - 1.00296i) q^{86} -1.53213i q^{87} +(-1.18259 - 3.09863i) q^{88} +(-9.98398 - 5.76425i) q^{89} +(1.72386 + 2.98582i) q^{90} +(-1.77709 - 1.02600i) q^{91} +(3.42976 + 5.94051i) q^{92} +(1.31071 + 2.27022i) q^{93} +0.772098 q^{94} +(-4.69720 + 14.2754i) q^{95} +1.00000i q^{96} +(-3.47315 + 2.00523i) q^{97} +(2.72079 + 4.71255i) q^{98} +(3.27478 + 0.525163i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 20 q^{2} - 20 q^{4} - 4 q^{5} - 40 q^{8} + 20 q^{9} + 4 q^{10} - 10 q^{13} + 12 q^{14} - 12 q^{15} - 20 q^{16} - 6 q^{17} + 40 q^{18} + 10 q^{19} + 8 q^{20} - 2 q^{21} + 8 q^{23} - 8 q^{25} - 20 q^{26}+ \cdots - 30 q^{98}+O(q^{100}) \) 40 * q + 20 * q^2 - 20 * q^4 - 4 * q^5 - 40 * q^8 + 20 * q^9 + 4 * q^10 - 10 * q^13 + 12 * q^14 - 12 * q^15 - 20 * q^16 - 6 * q^17 + 40 * q^18 + 10 * q^19 + 8 * q^20 - 2 * q^21 + 8 * q^23 - 8 * q^25 - 20 * q^26 + 12 * q^28 - 4 * q^29 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 12 * q^35 + 20 * q^36 + 8 * q^38 + 4 * q^40 + 2 * q^42 - 6 * q^43 - 8 * q^45 + 16 * q^46 + 10 * q^47 - 60 * q^49 - 16 * q^50 + 4 * q^51 - 10 * q^52 + 48 * q^53 + 16 * q^55 - 14 * q^57 - 8 * q^58 + 12 * q^60 - 6 * q^61 - 12 * q^63 + 40 * q^64 + 24 * q^65 - 4 * q^66 - 60 * q^67 + 12 * q^70 - 66 * q^71 - 20 * q^72 + 48 * q^73 + 12 * q^74 - 2 * q^76 + 8 * q^77 + 48 * q^79 - 4 * q^80 - 20 * q^81 + 4 * q^84 + 24 * q^85 - 6 * q^86 - 42 * q^89 - 4 * q^90 + 8 * q^92 - 12 * q^93 + 20 * q^94 - 8 * q^95 - 30 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more